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
In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented a...In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.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
Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider...Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..展开更多
Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the followi...Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].展开更多
In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div（h1（x）｜△u｜p-2△u）=d（x）｜u｜r-2u＋Gu（x,u,v） in Ω -div（h2（x）｜△u｜q-2△v）=f（x）｜v...In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div（h1（x）｜△u｜p-2△u）=d（x）｜u｜r-2u＋Gu（x,u,v） in Ω -div（h2（x）｜△u｜q-2△v）=f（x）｜v｜s-2v＋Gv（x,u,v） in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, N ≥ 2, 1 〈 r 〈 p ∞, 1〈 s 〈 q 〈 ∞; h1（x） and h2（x） are allowed to have ＂essential＂ zeroes at some points in Ω; d（x）｜u｜r-2u and f（x）｜v｜s-2v are small sources with Gu（x,u,v）, Gv（x,u,v） being their high-order perturbations with respect to （u, v） near the origin, respectively.展开更多
Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/...Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.展开更多
In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of...In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).展开更多
The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind o...The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind of the homogeneous type spaces.展开更多
This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are...This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).展开更多
Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are ob...Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.展开更多
Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix...Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.展开更多
文摘The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.
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.
文摘In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.
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 (11171254, 11271209)
文摘Let M be an n-dimensional complete noncompact Riemannian manifold with sectional curvature bounded from below, dμ = e^h（x） dV（x） the weighted measure and △μ,p the weighted p-Laplacian. In this paper we consider the non-linear elliptic equation △μ,pu=-λμ,p｜u｜^p-2ufor p ∈ （1, 2）. We derive a sharp gradient estimate for positive smooth solutions of this equation. As applications, we get a Harnack inequality and a Liouville type theorem..
基金supported by the Fundamental Research Fund for the Central Universities
文摘Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
基金Supported by the National Natural Science Foundation of China(11426122,11371153,and 11361029)the Specialized Research Fund for the Doctoral Program of Higher Education of Chinathe Natural Science Foundation of Jiangxi Province of China(20151BAB211003)
文摘In this article, we study the existence of infinitely many solutions to the degenerate quasilinear elliptic system -div（h1（x）｜△u｜p-2△u）=d（x）｜u｜r-2u＋Gu（x,u,v） in Ω -div（h2（x）｜△u｜q-2△v）=f（x）｜v｜s-2v＋Gv（x,u,v） in Ω, u=v=0 on δΩ where Ω is a bounded domain in RN with smooth boundary δΩ, N ≥ 2, 1 〈 r 〈 p ∞, 1〈 s 〈 q 〈 ∞; h1（x） and h2（x） are allowed to have ＂essential＂ zeroes at some points in Ω; d（x）｜u｜r-2u and f（x）｜v｜s-2v are small sources with Gu（x,u,v）, Gv（x,u,v） being their high-order perturbations with respect to （u, v） near the origin, respectively.
基金supported partly by the Natural Science Foundation from the Education Department of Anhui Province(KJ2017A847)The second author was supported by NSFC(11671039,11871101)NSFC-DFG(11761131002).
文摘Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.
文摘In this paper, we study the weighted (0,2;0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤3n-1 when the function values are prescribed at two sets of points namely the zeros of H n(x) and H ′ n(x) and the wieghted second derivative at the zeros of H n(x).
文摘The weighted HP(ω) spaces on the homogeneous type spaces have been defined in [1],in this paper we shall show the equivalence of various characterizations of HP (ω) on the certain groups that are the special kind of the homogeneous type spaces.
基金Partially supported by National Science Foundation of China(11426195,11771377)Natural Science Foundation of Jiangsu Province(BK20191435)。
文摘This paper deals with vanishing results for Lf^2 harmonic p-forms on complete metric measure spaces with a weighted p-Poincare inequality.Some results are without curvature assumptions for 1■p■n-1 and the others are with assumptions on lower bound of the m-Bakry-Emery Ricci curvature for p=1.These are weighted version for the corresponding results of the present author(J.Math.Anal.Appl.,2020,490).
基金SupportedbytheNationalNaturalScienceFoundationofChina (No .10 0 710 5 8)and (No .10 0 710 19)
文摘Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.
基金Supported by the National Natural Science Foundation of China (Grant No.12001434)The Natural Science Basic Research Program of Shaanxi Province (Grant No.2022JM-006)Chinese Universities Scientific Fund (Grant No.2452020021)
文摘Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.
