Entropy Numbers of Besov Classes of Generalized Smoothness on the Sphere  

作　　者：He Ping WANG Kai WANG Jing WANG 

机构地区：[1]School of Mathematical Sciences,Capital Normal University

出　　处：《Acta Mathematica Sinica,English Series》2014年第1期51-60,共10页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant Nos.10871132,11271263);Beijing Natural Science Foundation(Grant Nos.1102011,1132001);Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20091108110004)

摘　　要：We investigate the asymptotic behavior of the entropy numbers of Besov classes BBΩp,θ（Sd 1）of generalized smoothness on the sphere inL q（Sd 1）for 1≤p,q,θ≤∞,and get their asymptotic orders.We also obtain the exact orders of entropy numbers of Sobolev classesBWr p（Sd 1）inL q（Sd 1）whenpand/orqis equal to 1 or∞.This provides the last piece as far as exact orders of entropy numbers ofBWr p（Sd 1）inL q（Sd 1）are concerned.We investigate the asymptotic behavior of the entropy numbers of Besov classes BBΩp,θ（Sd 1）of generalized smoothness on the sphere inL q（Sd 1）for 1≤p,q,θ≤∞,and get their asymptotic orders.We also obtain the exact orders of entropy numbers of Sobolev classesBWr p（Sd 1）inL q（Sd 1）whenpand/orqis equal to 1 or∞.This provides the last piece as far as exact orders of entropy numbers ofBWr p（Sd 1）inL q（Sd 1）are concerned.

关 键 词：Entropy numbers modulus of smoothness Besov classes of generalized smoothness dis-cretizatation theorem 

分 类 号：O177.2[理学—数学]