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BOUNDEDNESS AND COMPACTNESS FOR THE COMMUTATOR OF THEω-TYPE CALDER′ON-ZYGMUND OPERATOR ON LORENTZ SPACE
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作者 陶祥兴 曾媛 喻晓 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1587-1602,共16页
In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The bo... In this paper,the authors consider theω-type Calder´on-Zygmund operator T_(ω)and the commutator[b,T_(ω)]generated by a symbol function b on the Lorentz space L^(p,r)(X)over the homogeneous space(X,d,μ).The boundedness and the compactness of the commutator[b,T_(ω)]on Lorentz space L^(p,r)(X)are founded for any p∈(1,∞)and r∈[1,∞). 展开更多
关键词 ω-type Calder´on-Zygmund operator COMMUTATORS lorentz space homogeneous space
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LITTLEWOOD-PALEY CHARACTERIZATIONS OF ANISOTROPIC HARDY-LORENTZ SPACES 被引量:5
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作者 刘军 杨大春 袁文 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期1-33,共33页
Let p∈(0, 1], q∈(0, ∞] and A be a general expansive matrix on Rn. Let HAp,q (Rn) be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article,... Let p∈(0, 1], q∈(0, ∞] and A be a general expansive matrix on Rn. Let HAp,q (Rn) be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize HAp,q(Rn) in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley gλ*-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space Lp,q(Rn). All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on Rn. Moreover, the range of λ in the gλ*-function characterization of HAp,q (Rn) coincides with the best known one in the classical Hardy space Hp(Rn) or in the anisotropic Hardy space HAp (Rn). 展开更多
关键词 lorentz space anisotropic Hardy-lorentz space expansive matrix Calderón reproducing formula Littlewood-Paley function
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MULTIPLIERS AND RELATIVE COMPLETION IN WEIGHTED LORENTZ SPACES 被引量:2
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作者 CenapDuyar A.TuranGuerkanli 《Acta Mathematica Scientia》 SCIE CSCD 2003年第4期467-476,共10页
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
关键词 Banach module weighted L~P(G) space lorentz space weighted lorentz space MULTIPLIER
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some Results on Embedding Spaces of Sobolev Type into Lorentz Spaces
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作者 姜明 《Journal of Beijing Institute of Technology》 EI CAS 1993年第2期103-108,共6页
Lorentz spaces L^(s,l) provide a deeper insight into integrable functions than L^s spaces do. Various results of the embedding of the following anisotropic spaces B_(p,).~ _p^and Ⅳ_p~ in- to L^(s,l) together with a ... Lorentz spaces L^(s,l) provide a deeper insight into integrable functions than L^s spaces do. Various results of the embedding of the following anisotropic spaces B_(p,).~ _p^and Ⅳ_p~ in- to L^(s,l) together with a counterexample are obtained. 展开更多
关键词 Sobolev space / anisotropic spaces lorentz space
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THE DUAL OF NONCOMMUTATIVE LORENTZ SPACES 被引量:3
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作者 韩亚洲 Turdebek N. Bekjan 《Acta Mathematica Scientia》 SCIE CSCD 2011年第5期2067-2080,共14页
We prove some noncommutative analogues of the classical results about dual spaces of the classical Lorentz spaces.
关键词 dual spaces noncommutayive lorentz spaces operator algebras
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SZEG TYPE FACTORIZATION THEOREM FOR NONCOMMUTATIVE HARDY-LORENTZ SPACES 被引量:5
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作者 邵晶晶 韩亚洲 《Acta Mathematica Scientia》 SCIE CSCD 2013年第6期1675-1684,共10页
We introduce noncommutative Hardy-Lorentz spaces and give the Szegō and inner-outer type factorizations of these spaces.
关键词 subdiagonal algebras noncommutative Hardy-lorentz spaces Szegō factor-ization outer operators
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WEAK ATOMIC DECOMPOSITIONS OF MARTINGALE HARDY-LORENTZ SPACES AND APPLICATIONS 被引量:2
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作者 任颜波 郭铁信 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期1157-1166,共10页
In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lo... In this article, we establish some atomic decomposition theorems for martin- gale Hardy-Lorentz spaces. As applications, with the help of weak atomic decompositions, some interpolation theorems for martingale Hardy-Lorentz spaces are proved. 展开更多
关键词 Martingale Hardy-lorentz space weak atom atomic decomposition inter- polation
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MULTIPLIERS AND TENSOR PRODUCTS OF L(p,q) LORENTZ SPACES 被引量:1
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作者 Hakan Avci A.Turan Gürkanli 《Acta Mathematica Scientia》 SCIE CSCD 2007年第1期107-116,共10页
Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space. L(p1, q1)(G) to L(p'2, q'2)(G). For this reason, the authors define the ... Let G be a locally compact abelian group. The main purpose of this article is to find the space of multipliers from the Lorentz space. L(p1, q1)(G) to L(p'2, q'2)(G). For this reason, the authors define the space A p1,q1^ p2,p2(G), discuss its properties and prove that the space of multipliers from L(p1, q1)(G) to L(p'2, q'2)(G) is isometrically isomorphic to the dual of A p1,q1^p2,q2 (G). 展开更多
关键词 lorentz space Banach module MULTIPLIER
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On M–Term Approximations of the Nikol'skii–Besov Class in the Lorentz Spaces
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作者 G.Akishev 《Analysis in Theory and Applications》 CSCD 2017年第3期267-286,共20页
In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol'skii's and Besov's classes in the Lore... In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol'skii's and Besov's classes in the Lorentz space with the mixed norm. 展开更多
关键词 lorentz space Besov's class approximation.
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On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm
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作者 G.Akishev 《Analysis in Theory and Applications》 2013年第4期358-372,共15页
In this paper, Lorentz space of functions of several variables and Besov's class are considered. We establish an exact approximation order of Besov's class by partial sums of Fourier's series for multiple trigonome... In this paper, Lorentz space of functions of several variables and Besov's class are considered. We establish an exact approximation order of Besov's class by partial sums of Fourier's series for multiple trigonometric system. 展开更多
关键词 lorentz space Besov's class approximation.
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Complete Spacelike Hypersurfaces with Constant Scalar Curvature in Locally Symmetric Lorentz Spaces
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作者 张士诚 吴报强 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第2期266-275,共10页
The complete space-like hypersurfaces with constant normal saclar curvature is discussed in a locally symmetric Lorentz space. A classified theorem is obtained by the operator L1 introduced by S Y Cheng and S T Yau [3].
关键词 locally symmetric lorentz space constant saclar curvature space-like hypersurfaces second fundamental form
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Linear Weingarten spacelike hypersurface in locally symmetric Lorentz space
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作者 Wang Peijun Chao Xiaoli Bai Miaomiao 《Journal of Southeast University(English Edition)》 EI CAS 2018年第2期276-280,共5页
The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an... The rigidity of spacelike hypersurface Mn immersed in locally symmetric space M1n+1 is investigated,where the(normalized)scalar curvature R and mean curvature H of Mn satisfy R=aH+b,and a,b are real constants.First,an estimate of the upper bound of the function L(nH)is given,where L is a second-order differential operator.Then,under the assumption that the square norm of the second fundamental form is bounded by a given positive constant,it is proved that Mn must be either totally umbilical or contain two distinct principle curvatures,one of which is simple.Moreover,a similar result is obtained for complete noncompact spacelike hypersurfaces in locally symmetric Einstein spacetime.Hence,some known rigidity results for hypersurface with constant scalar curvature are extended for the linear Weingarten case. 展开更多
关键词 spacelike hypersurface linear Weingarten locally symmetric lorentz space
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Existence of Weak Solutions of Two-dimensional Euler Equations with Initial Vorticity in Lorentz Space L_(2,1)(R^2)
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作者 酒全森 《Northeastern Mathematical Journal》 CSCD 2000年第3期291-298,共8页
Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional... Some estimates on 2-D Euler equations are given when initia l vorticity ω0 belongs to a Lorentz space L(2,1). Then based on these estimates, it is proved that there exist global weak solutions of two dim ensional Euler equations when ω0∈L(2,1). 展开更多
关键词 EXISTENCE Euler equations weak solution lorentz space
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Regularity for 3-D MHD Equations in Lorentz Space L^(3,∞)
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作者 Xiangao Liu Yueli Liu Zixuan Liu 《Communications in Mathematical Research》 CSCD 2023年第1期107-135,共29页
.The regularity for 3-D MHD equations is considered in this paper,it is proved that the solutions(v,B,p)are Holder continuous if the velocity field v∈L^(∞)(0,T;L^(3,∞)_(x)(R^(3))with local small condition r^(-3)|{x... .The regularity for 3-D MHD equations is considered in this paper,it is proved that the solutions(v,B,p)are Holder continuous if the velocity field v∈L^(∞)(0,T;L^(3,∞)_(x)(R^(3))with local small condition r^(-3)|{x∈B_(r)(x_(0):|v(x,t_(0))|>εr^(-1)}|≤ε and the magnetic field B∈L^(∞)(0,T;VMO^(-1)(R^(3)). 展开更多
关键词 lorentz space backward uniqueness MHD equations.
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Cartan-Hadamard流形上关于Lorentz范数的Trudinger-Moser不等式
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作者 张佳杰 《数学杂志》 2024年第4期283-292,共10页
本文研究了Cartan-Hadamard流形上带Lorentz范数的Trudinger-Moser不等式.利用了相关格林函数的逐点估计以及O’Neil不等式,我们得到了该不等式的最佳常数,推广了相应欧氏空间上的结果.
关键词 Trudinger-Moser不等式 lorentz空间 RIEMANNIAN流形 负曲率 最佳常数
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The Vertical Projection Model of Hyperbolic Space and Geometric Illustration of Special Relativity
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作者 Weiyu Luo 《Journal of Applied Mathematics and Physics》 2024年第1期72-90,共19页
In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyp... In this article, new visual and intuitive interpretations of Lorentz transformation and Einstein velocity addition are given. We first obtain geometric interpretations of isometries of vertical projection model of hyperbolic space, which are the analogues of the geometric construction of inversions with respect to a circle on the complex plane. These results are then applied to Lorentz transformation and Einstein velocity addition to obtain geometric illustrations. We gain new insights into the relationship between special relativity and hyperbolic geometry. 展开更多
关键词 lorentz Transformation Einstein Velocity Addition Hyperbolic space
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LORENTZ MARTINGALE SPACES AND INTERPOLATION 被引量:7
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作者 范利萍 焦勇 刘培德 《Acta Mathematica Scientia》 SCIE CSCD 2010年第4期1143-1153,共11页
In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation... In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role. 展开更多
关键词 MARTINGALE lorentz space WEIGHT INTERPOLATION
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An Off-Diagonal Marcinkiewicz Interpolation Theorem on Lorentz Spaces 被引量:2
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作者 Yi Yu LIANG Li Guang LIU Da Chun YANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第8期1477-1488,共12页
Let (X, μ) be a measure space. In this paper, using some ideas from Grafakos and Kalton, the authors establish an off-diagonal Marcinkiewicz interpolation theorem for a quasilinear operator T in Lorentz spaces L^P,... Let (X, μ) be a measure space. In this paper, using some ideas from Grafakos and Kalton, the authors establish an off-diagonal Marcinkiewicz interpolation theorem for a quasilinear operator T in Lorentz spaces L^P,q(X) with p, q £ (0, ∞], which is a corrected version of Theorem 1.4.19 in [Grafakos, L.: Classical Fourier Analysis, Second Edition, Graduate Texts in Math., No. 249, Springer, New York, 2008] and which, in the case that T is linear or nonnegative sublinear, p £ [1, ∞) and q £ [l,∞), was obtained by Stein and Weiss [Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, N.J., 1971]. 展开更多
关键词 Quasilinear operator Marcinkiewicz interpolation theorem lorentz space restricted weak type estimate
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Anisotropic Hardy-Lorentz spaces and their applications 被引量:13
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作者 LIU Jun YANG DaChun YUAN Wen 《Science China Mathematics》 SCIE CSCD 2016年第9期1669-1720,共52页
Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish... Let p ∈(0, 1], q ∈(0, ∞] and A be a general expansive matrix on Rn. We introduce the anisotropic Hardy-Lorentz space H^(p,q)_A(R^n) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on Rn.As applications, we first prove that Hp,q A(Rn) is an intermediate space between H^(p1,q1)_A(Rn) and H^(p2,q2)_A(R^n) with 0 < p1 < p < p2 < ∞ and q1, q, q2 ∈(0, ∞], and also between H^(p,q1)_A(Rn) and H^(p,q2)_A(R^n) with p ∈(0, ∞)and 0 < q1 < q < q2 ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H^(p,q)_A(R^n) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calder′on-Zygmund operators from H^(p,∞)_A(R^n) to the weak Lebesgue space L^(p,∞)(R^n)(or to H^p_A(R^n)) in the ln λcritical case, from H^(p,q)_A(R^n) to L^(p,q)(R^n)(or to H^(p,q)_A(R^n)) with δ∈(0,(lnλ)/(ln b)], p ∈(1/(1+,δ),1] and q ∈(0, ∞], as well as the boundedness of some Calderon-Zygmund operators from H^(p,q)_A(R^n) to L^(p,∞)(R^n), where b := | det A|,λ_:= min{|λ| : λ∈σ(A)} and σ(A) denotes the set of all eigenvalues of A. 展开更多
关键词 lorentz space anisotropic Hardy-lorentz space expansive matrix Calder′on reproducing formula grand maximal function atom molecule Calder′on-Zygmund operator
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On Mixed Pressure-Velocity Regularity Criteria to the Navier-Stokes Equations in Lorentz Spaces 被引量:1
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作者 Hugo BEIRAO da VEIGA Jiaqi YANG 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2021年第1期1-16,共16页
In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes th... In this paper the authors derive regular criteria in Lorentz spaces for LerayHopf weak solutions v of the three-dimensional Navier-Stokes equations based on the formal equivalence relationπ≌|v|^(2),whereπdenotes the fluid pressure and v denotes the fluid velocity.It is called the mixed pressure-velocity problem(the P-V problem for short).It is shown that if(π/(e-^|(x)|^(2)+|v|^(θ)∈L^(p)(0,T;L^(q,∞)),where 0≤θ≤1 and 2/p+3/q=2-θ,then v is regular on(0,T].Note that,ifΩ,is periodic,e^(-|x|)^(2) may be replaced by a positive constant.This result improves a 2018 statement obtained by one of the authors.Furthermore,as an integral part of the contribution,the authors give an overview on the known results on the P-V problem,and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin(L-P-S for short)type. 展开更多
关键词 Navier-Stokes equations Pressure≌square velocity Regularity criteria lorentz spaces
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