Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weight...Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.展开更多
众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等...众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。展开更多
The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regulari...The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.展开更多
Banach 空间 X 的凸系数ε_0(X)是表征此空间单位球凸性程度的重要几何常数,称δ_x(a)=in{1-‖x+y/2‖:‖x‖=‖y‖=‖x-y/a‖=1},(0≤a≤2)为凸性模,称ε_0(X)=sup{a:δ_x(a)=0}为凸性系数.容易看到:ε_0(X)=0等价于 X 一致凸;ε_0(X)=...Banach 空间 X 的凸系数ε_0(X)是表征此空间单位球凸性程度的重要几何常数,称δ_x(a)=in{1-‖x+y/2‖:‖x‖=‖y‖=‖x-y/a‖=1},(0≤a≤2)为凸性模,称ε_0(X)=sup{a:δ_x(a)=0}为凸性系数.容易看到:ε_0(X)=0等价于 X 一致凸;ε_0(X)=2等价于 X 区不一致非方.本文讨论了赋 Orlicz 范数的 Orlicz 空间,L~φ的凸系数ε_0(L~φ),给出了一个简单估计式和一个复杂的计算程序.展开更多
In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
文摘Let D be the open unit disk in the complex plane C. For a〉 -1, let dAa（z）=（1 ＋a） （1 -｜z}^2） ^a da（z）be the weighted Lebesgue measure on ]D. For a positive function ω ∈ L^1（D,dAa）, the generalized weighted Bergman-Orlicz spaceA^ψω（D,dAa）is｜｜f｜｜ω^ψ=∫Dψ｜F（z）｜ω（z）dA^（z） 〈 ∞,where q; is a strictly convex Orlicz function that satisfies other technical hypotheses. Let G be a measurable subset of D, we say G satisfies the reverse Carleson condition for A^ψω （D, dAa） if there exists a positive constant C such that ∫Gψ（f（z））ω（z）dAa（z）≥C∫Dψ（｜f（z）dAa（z）.for all f ∈ .A^ψω （D,dAa）. Let μ be a positive Borel measure, we say μ satisfies the direct Carleson condition if there exists a positive constant M such that for all f∈Aψ^ω （D,dAa）,∫Dψ（｜f（z）｜）dμ（z）≤M∫Dψ（｜f（z）｜）ω（z）dAa（a）.In this paper, we study the direct and reverse Carleson condition on the generalized weighted Bergman-Orlicz space Aω^ψ（D,dAa）.We present conditions on the set G such that＇the reverse Carleson condition＇holds. ＂Moreover, we give a sufficient condition for the finite positive Borel measure μ to satisfy the direct carleson condition on the generalized weighted Bergman-Orlicz spaces.
文摘众所周知,Orlicz范数与Luxemburg范数是等价的。2011年,BANG H H,HOANG N V,HUY V N,研究了由N函数生成的Orlicz空间中Orlicz范数与Luxemburg范数等价的最佳常数,本文将他们的结果推广到由一般Orlicz函数中Orlicz范数与Luxemburg范数等价的最佳常数。与此同时得到了1<inf k>0∶1 k(1+IΦ(kx))=1及sup k>0∶1 k(1+IΦ(kx))=1<∞的等价条件。
基金Supported by the NNSF of China(10771110,11171306)Supported by the the New Century 151 Talent Project of Zhejiang Province
文摘The purpose of this paper is to give the element proof of the regularity estimates in Orlicz classes for the second order derivatives of the solutions to the general second order elliptic equations.The global regularities in Orlicz for the second order derivatives of the solutions of the Dirichlet problems are also given.
文摘Banach 空间 X 的凸系数ε_0(X)是表征此空间单位球凸性程度的重要几何常数,称δ_x(a)=in{1-‖x+y/2‖:‖x‖=‖y‖=‖x-y/a‖=1},(0≤a≤2)为凸性模,称ε_0(X)=sup{a:δ_x(a)=0}为凸性系数.容易看到:ε_0(X)=0等价于 X 一致凸;ε_0(X)=2等价于 X 区不一致非方.本文讨论了赋 Orlicz 范数的 Orlicz 空间,L~φ的凸系数ε_0(L~φ),给出了一个简单估计式和一个复杂的计算程序.
文摘In this paper, we present and discuss the topology of modular spaces using the filter base and we then characterize closed subsets as well as its regularity.
