Cn中单位球面上的不变g-函数及BMOA

设B是Cn中的单位球,S是Cn中的单位球面,(g)(f)是定义在S上的不变g-函数.设f∈BMOA,若存在正测度集E(∪)S,使(g)(f)＜+∞在E上成立,则(g)(f)＜+∞在S上几乎处处成立,同时(g)(f)∈BMO(S)且存在常数C,使得‖(g)(f)‖*≤C‖f‖*.     

C~n中单位球上的面积积分与BMO

设B是Cn中的单位球,S是Cn中的单位球面,Sα(f)是B上的面积积分.设f∈BMOA, 若存在正测度集E(?)S,使Sα(f)<∞在E上成立,则Sα(f)<∞在S上几乎处处成立,同时 Sα(f)∈ BMO(S)且存在常数C,使得||Sαf||*≤C||f||*.     

关于g-函数和弱g-函数的两个结果

利用g-函数和弱g-函数给出了度量空间的新刻划,回答了Nagata的问题.     

C~n中单位球上一些全纯函数空间的特征

对Ｐ＞０,－∞＜ｓ＜∞,Ｃｎ中的球Ｂ上的Ｂｅｒｇｍａｎ空间Ｌｐａ（Ｂ）等同于Ｂ上满足 的全纯函数ｆ的全体当且仅当ｓ＞ ｍａｘ｛０, ２－ ｐ｝．此处和λ分别是 Ｂ上的不变梯度和不变测度．对Ｂ上的Ｂｌｏｃｈ函数空间,也有着相应的特征刻划．作为这些结果的应用,本文解决了欧阳才衡、杨微生和赵如汉的一个猜测．     

Littlewood-Paley g-函数与加权BMO函数

设gφ,b是Littlewood-Paley g-函数与b生成的交换子.本文证明了若α,β属于Muckenhoupt A_p权函数类,1相似文献   

Littlewood-Paley g-函数交换子的加权估计

设g_(φ,b)是Littlewood-Paley g-函数与b生成的交换子,ω∈A_1.证明了若b属于加权BMO空间BMO(ω),则g_(φ,b)是L~p(ω)到L~p(ω~(1-p))(1p∞)有界的;若b属于加权Lipschitz空间Lip_β(ω)(0β1),则g_(φ,b)是L~p(ω)到L~q(ω~(1-q))的有界算子,其中1pq∞,1/q=1/p-β/n.     

单位球上全纯函数空间的系数乘子

本文给出了C^n中超球B上Hardy空间H^p,Bergman空间Lα^p,Bloch空间β，Besov空间Bp及Lipschitz空间Ak^p之间的系数乘子。     

Littlewood-Paley g-函数交换子的Hardy型估计

证明了当q>1时,Littlewood-Paley g-函数与LMO(BMO的一个子空间)函数的交换子g_(Ψ,b)是局部Hardy空间h~1(R~n)到空间h~1(R~n)+L~q(R~n)的一个连续映射.     

Cn中单位球上的面积积分与BMO

设B是Cn中的单位球,S是Cn中的单位球面,Sα(f)是B上的面积积分.设f∈BMOA,若存在正测度集E S,使Sα(f)＜∞在E上成立,则Sα(f)＜∞在S上几乎处处成立,同时Sα(f)∈BMO(S)且存在常数C,使得‖Sαf‖*≤‖Cf‖*.     

C^n中单位球上Mobius不变Besov空间中函数的增长性

本文主要讨论Ｃ＾ｎ中单位球上Ｍｏｂｉｕｓ不变Ｂｅｓｏｖ空间中函数的增长性并给出其Ｔａｙｌｏｒ系数的估计．     

The Equivalence of BMOA and VMOA on the Unit Ball of C n

１ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＢｂｅｔｈｅｏｐｅｎｕｎｉｔｂａｌｉｎＣｎａｎｄＳｂｅｉｔｓｂｏｕｎｄａｒｙ．ＬｅｔσｂｅｔｈｅｒｏｔａｔｉｏｎｉｎｖａｒｉａｎｔｐｒｏｂａｂｉｌｉｔｙｍｅａｓｕｒｅｏｎＳ．Ｆｏｒζ∈Ｓａｎｄδ＞０,ｌｅｔＱ（ζ,δ）...     

Herz型空间中的Littlewood-Paley g函数

本文研究了包含 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ ｇ函数在内的一大类次线性算子从 Ｈｅｒｚ 空间到弱Ｈｅｒｚ空间ＷＫ中的有界 性;而当时,我们得到了ｇ函数从 Ｈｅｒｚ型 Ｈａｒｄｙ空间 ＨＫ（Ｒｎ）到 Ｈｅｒｚ空间或弱Ｈｅｒｚ空间ＷＫ（Ｒｎ）中的有界性．     

齐型空间上的Lipschitz函数与Littlewood－Paley g－函数

在θ阶正规齐型空间上，如果算子列｛Ｓｋ｝ｋ∈Ｚ是恒等逼近，Ｄｋ＝Ｓｋ－Ｓｋ－１；本文给出一个用｛Ｄｋ｝ｋ∈Ｚ表达的ｆ∈Ｌｉｐα（Ｌｉｐｓｃｈｉｔｚ函数类，０＜α＜θ）的充分必要条件．作为其推论得到，对于ｆ∈ＬＩｐα，其Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙｇ函数ｇ（ｆ）（Ｘ）或者处处为无穷大，或者在Ｌｉｐα上有界．     

Compactness of composition operators on BMOA and VMOA

We give a new and simple compactness condition for composition operators on BMOA,the space of all analytic functions of the bounded mean oscillation on the unit disk.Using our results one may immediately obtain that compactness of a composition operator on BMOA implies its compactness on the Bloch space as well as on the Hardy space.Similar results on VMOA are also given.     

齐型空间上的Lipschitz函数与Littlewood－Paley g－函数

在θ阶正规齐型空间上，如果算子列｛Ｓｋ｝ｋ∈Ｚ是恒等逼近，Ｄｋ＝Ｓｋ－Ｓｋ－１；本文给出一个用｛Ｄｋ｝ｋ∈Ｚ表达的ｆ∈Ｌｉｐα（Ｌｉｐｓｃｈｉｔｚ函数类，０＜α＜θ）的充分必要条件．作为其推论得到，对于ｆ∈ＬＩｐα，其Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙｇ函数ｇ（ｆ）（Ｘ）或者处处为无穷大，或者在Ｌｉｐα上有界．     

The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc

The main results of this note prove that the generalized Libera operator is bounded on the Besov mixed-norm space as well as on the spaces BMOA and VMOA on the unit disk. The compactness of the operator on is also studied.     

Polynomial Interpolation on the Unit Sphere and on the Unit Ball

The problem of interpolation on the unit sphere S ^d by spherical polynomials of degree at most n is shown to be related to the interpolation on the unit ball B ^d by polynomials of degree n. As a consequence several explicit sets of points on S ^d are given for which the interpolation by spherical polynomials has a unique solution. We also discuss interpolation on the unit disc of R ² for which points are located on the circles and each circle has an even number of points. The problem is shown to be related to interpolation on the triangle in a natural way.     

Invariant Minimal Unit Vector Fields on Lie Groups

We provide a new characterization of invariant minimal unit vector fields on Lie groups and use it to construct some new examples. In particular, we determine all these vector fields on three-dimensional Lie groups.     

The role of BMOA in the boundedness of weighted composition operators on the unit ball

We study the weighted composition operators Wh,on Hardy space H2(B) whenever h ∈ BMOA(resp.h ∈ VMOA).Analogous results are given for Hp(B) spaces and the scale of weighted Bergman spaces.In the latter case,BMOA is replaced by the Bloch space(resp.VMOA by the little Bloch space).