For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f...For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.展开更多
Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting...Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.展开更多
This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schem...This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.展开更多
This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of th...This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).展开更多
It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to ...It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).展开更多
In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of si...In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given.展开更多
In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exac...In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.展开更多
In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^* on the w...In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^* on the weighted amalgam spaces (Lω^q,L^p)^α(R^n)as 1〈q≤α〈p≤∞.展开更多
Let x (xn)≥1 be a martingale on a noncommutative probability space n (M, r) and (wn)n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = (x.)n≥1 converges in E(M...Let x (xn)≥1 be a martingale on a noncommutative probability space n (M, r) and (wn)n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = (x.)n≥1 converges in E(M) if and only if (σn(x)n≥1 converges in E(.hd), where E(A//) is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn(x) is given by σn(x) = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E(Ad) has absolutely continuous norm, then, (an(x))≥1 converges in E(.M) if and only if x = (Xn)n≥1 is uniformly integrable and its limit in measure topology x∞∈ E(M).展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A o...Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.展开更多
In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;(R;) ( -1 ≤α≤0), defined by H;f(x)=∫R;Φ(u)f(A(u)x)du,where Φ∈L;oc;(R;),A(u) = (α;(u));is a...In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;(R;) ( -1 ≤α≤0), defined by H;f(x)=∫R;Φ(u)f(A(u)x)du,where Φ∈L;oc;(R;),A(u) = (α;(u));is a 2×2 matrix, and each α;is a measurablefunction.We obtain that HΦ,A is bounded from H;(R;) ( -1≤α≤0) to itself, if∫R2|Φ(u)‖det A;(u)|‖A(u)‖;ln(1+‖A;(u)‖;/|det A;(u)|)du<∞.This result improves some known theorems, and in some sense it is sharp.展开更多
In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q(w;R^n1×R^n2) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we estab...In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q(w;R^n1×R^n2) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that (Fp'q)* = CMOp^-a,q' for 0 ~p≤ 1.展开更多
This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to ...This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a t...Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).展开更多
In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈...In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈 1 and w ∈ A1.展开更多
Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedn...Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k(w) when the symbol b belongs to BMO(Rn) or the homogeneous Lipschitz space.展开更多
In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the ...In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T>0.展开更多
Let α∈(0,∞ ), p, q ∈[1, ∞), s be a nonnegative integer, and ω∈ A1(Rn) (tne class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey- Campanato space L(α, p, q, s, ...Let α∈(0,∞ ), p, q ∈[1, ∞), s be a nonnegative integer, and ω∈ A1(Rn) (tne class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey- Campanato space L(α, p, q, s, ω; Rn) and obtain its equivalence on different p∈ [1, β) and 1 integers s ≥[nα] (the integer part of nα), whereβ = (1/q - α)-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A(α, q, w; Rn) and prove that L(a, p, q, s, w; Rn)С ∧(α, q, w; Rn) when α ∈ (0, ∞), s ≥[nα], and p∈ [1,β).展开更多
文摘For analytic functions u,ψin the unit disk D in the complex plane and an analytic self-mapφof D,we describe in this paper the boundedness and compactness of product type operators T_(u,ψ,φ)f(z)=u(z)f(φ(z))+ψ(z)f'(φ(z)),z∈D,acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.
文摘Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.
文摘This study introduces the Orbit Weighting Scheme(OWS),a novel approach aimed at enhancing the precision and efficiency of Vector Space information retrieval(IR)models,which have traditionally relied on weighting schemes like tf-idf and BM25.These conventional methods often struggle with accurately capturing document relevance,leading to inefficiencies in both retrieval performance and index size management.OWS proposes a dynamic weighting mechanism that evaluates the significance of terms based on their orbital position within the vector space,emphasizing term relationships and distribution patterns overlooked by existing models.Our research focuses on evaluating OWS’s impact on model accuracy using Information Retrieval metrics like Recall,Precision,InterpolatedAverage Precision(IAP),andMeanAverage Precision(MAP).Additionally,we assessOWS’s effectiveness in reducing the inverted index size,crucial for model efficiency.We compare OWS-based retrieval models against others using different schemes,including tf-idf variations and BM25Delta.Results reveal OWS’s superiority,achieving a 54%Recall and 81%MAP,and a notable 38%reduction in the inverted index size.This highlights OWS’s potential in optimizing retrieval processes and underscores the need for further research in this underrepresented area to fully leverage OWS’s capabilities in information retrieval methodologies.
文摘This paper is devoted to studying the behaviors of the fractional type Marcinkiewicz integralsμΩ,βand the commutatorsμΩ,βb generated byμΩ,βwith b b∈Lloc(Rn)on weighted Hardy spaces.Under the assumption of that the homogeneous kernelΩsatisfies certain regularities,the authors obtain the boundedness ofμΩ,βfrom the weighted Hardy spaces Hωpp(Rn)to the weighted Lebesgue spaces Lωqq(Rn)for n/(n+β)≤<p≤1 with 1/q=1/p-β/n,as well as the same(Hωpp,Lωqq)-boudedness ofμΩ,βb when b belongs to BMOωp,p(Rn),which is a non-trivial subspace of BMO(Rn).
文摘It is proved that, for the nondivergence elliptic equations Σi,jn=1aijuxixj=f, if f belongs to the generalized Morrey spaces Lp, (w), then uxixj ∈ Lp, (w), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp, (w).
基金Supported by the National Natural Science Foundation of China(11561057,11226104)the Jiangxi Natural Science Foundation of China(20151BAB211002)+1 种基金the Science Foundation of Jiangxi Education Department(GJJ151054)the Scientific Research project of Shangrao Normal University
文摘In this paper, the authors prove the weighted boundedness of singular integral and fractional integral with a rough kernel on the weighted λ-central Morrey space. Moreover, the weighted estimate for commutators of singular integral with a rough kernel on the weighted λ-central Morrey space is also given.
基金supported by the National Natural Science Foundation of China (10901158)
文摘In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.
基金supported in part by National Natural Foundation of China (Grant No. 11161042 and No. 11071250)
文摘In this paper, we shall deal with the boundedness of the Littlewood-Paley operators with rough kernel. We prove the boundedness of the Lusin-area integral μΩs and Littlewood-Paley functions μΩ and μλ^* on the weighted amalgam spaces (Lω^q,L^p)^α(R^n)as 1〈q≤α〈p≤∞.
基金supported by the National Natural Science Foundation of China (11071190)
文摘Let x (xn)≥1 be a martingale on a noncommutative probability space n (M, r) and (wn)n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = (x.)n≥1 converges in E(M) if and only if (σn(x)n≥1 converges in E(.hd), where E(A//) is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn(x) is given by σn(x) = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E(Ad) has absolutely continuous norm, then, (an(x))≥1 converges in E(.M) if and only if x = (Xn)n≥1 is uniformly integrable and its limit in measure topology x∞∈ E(M).
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘Let G be a locally compact Abelian group with Haar measure μ. In the present paper, first the authors discussed some properties of weighted Lorentz space. Then they defined the relative completion A of a subspace A of the weighted Lorentz space, and showed that the space of the multipliers from L_w~1,(G) to A is algebrically isomorphic and homeomorphic to A.
基金Supported by the National Natural Science Foundation of China(11671363,11471288)
文摘In this paper, we consider the two-dimensional Hausdorff operators on the power weighted Hardy space H;(R;) ( -1 ≤α≤0), defined by H;f(x)=∫R;Φ(u)f(A(u)x)du,where Φ∈L;oc;(R;),A(u) = (α;(u));is a 2×2 matrix, and each α;is a measurablefunction.We obtain that HΦ,A is bounded from H;(R;) ( -1≤α≤0) to itself, if∫R2|Φ(u)‖det A;(u)|‖A(u)‖;ln(1+‖A;(u)‖;/|det A;(u)|)du<∞.This result improves some known theorems, and in some sense it is sharp.
基金Supported by NNSF of China grants(11501308,11271209,11371370)Jiangsu Government Scholarship for Overseas Studies
文摘In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q(w;R^n1×R^n2) based on the Frazier and Jawerth' method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that (Fp'q)* = CMOp^-a,q' for 0 ~p≤ 1.
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘This paper deals with the boundedness and compactness of the weighted composition operators from the F(p, q, s) spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞( or little Bers-type spaces Hv,o∞ ), where v is normal.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
文摘Let G be a locally compact unimodular group with Haar measure rmdx and ω be the Beurling's weight function on G (Reiter, [10]). In this paper the authors define a space Aωp,q (G) and prove that Aωp,q (G) is a translation invariant Banach space. Fur- thermore the authors discuss inclusion properties and show that if G is a locally compact abelian group then Aωp,q (G) admits an approximate identity bounded in Lω1 (G). It is also proved that the space Lωp (G) Lω1 Lωq (G) is isometrically isomorphic to the space Aωp,q (G) and the space of multipliers from Lωp (G) to Lq-1, (G) is isometrically isomorphic to the dual of the space Aωp,q (G) iff G satisfies a property Ppq. At the end of this work it is showed that if G is a locally compact abelian group then the space of all multipliers from Lω1 (G) to Aωp,q (G) is the space Aωp,q (G).
文摘In this paper, we will obtain the weak type estimates of intrinsic square func- tions including the Lusin area integral, Littlewood-Paley g-function and g^-function on the weighted Morrey spaces L^1,k (w) for 0〈k〈 1 and w ∈ A1.
文摘Let L be the infinitesimal generator of an analytic semigroup on L^2 (R^n) with Gaussian kernel bound, and let L^-α/2 be the fractional integrals of L for 0 〈 α 〈 n. In this paper, we will obtain some boundedness properties of commutators [b, L^-α/2] on weighted Morrey spaces L^p,k(w) when the symbol b belongs to BMO(Rn) or the homogeneous Lipschitz space.
文摘In this paper, we investigate the existence and uniqueness of weak solutions for a new class of initial/boundary-value parabolic problems with nonlinear perturbation term in weighted Sobolev space. By building up the compact imbedding in weighted Sobolev space and extending Galerkin’s method to a new class of nonlinear problems, we drive out that there exists at least one weak solution of the nonlinear equations in the interval [0,T] for the fixed time T>0.
基金supported by the National Natural Science Foundation of China(10871025)
文摘Let α∈(0,∞ ), p, q ∈[1, ∞), s be a nonnegative integer, and ω∈ A1(Rn) (tne class of Muckenhoupt's weights). In this paper, we introduce the generalized weighted Morrey- Campanato space L(α, p, q, s, ω; Rn) and obtain its equivalence on different p∈ [1, β) and 1 integers s ≥[nα] (the integer part of nα), whereβ = (1/q - α)-1 when α 〈 1/qorβ= ∞ when α ≥1/q We then introduce the generalized weighted Lipschitz space A(α, q, w; Rn) and prove that L(a, p, q, s, w; Rn)С ∧(α, q, w; Rn) when α ∈ (0, ∞), s ≥[nα], and p∈ [1,β).