Jackson's Theorem on Bounded Symmetric Domains  

作　　者：Ming Zhi WANG Guang Bin REN 

机构地区：[1]School of Science, Huzhou Teachers College, Huzhou 313000, P. R. China [2]Department of Mathematics, University of Science and Technology of China, Hefei 230026, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第8期1391-1404,共14页数学学报（英文版）

基　　金：Partially supported by the NNSF of China(No.10471134);SRFDP;NCET

摘　　要：Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson＇s theorem to several complex variables：Eκ（f,X）≤ω（1/k,f,X）, where Eκ（f,X） is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω（1/k,f,X） is the corresponding modulus of continuity.Polynomial approximation is studied on bounded symmetric domain Ω in C^n for holomorphic function spaces X such as Bloch-type spaces, Bergman-type spaces, Hardy spaces, Ω algebra and Lipschitz space. We extend the classical Jackson＇s theorem to several complex variables：Eκ（f,X）≤ω（1/k,f,X）, where Eκ（f,X） is the deviation of the best approximation of f ∈X by polynomials of degree at most k with respect to the X-metric and ω（1/k,f,X） is the corresponding modulus of continuity.

关 键 词：bounded symmetric domains Bergman spaces polynomial approximation 

分 类 号：O17[理学—数学]