Entropy Numbers of Besov Classes of Generalized Smoothness on the Sphere

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...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2014, Vol.30 (1), p.51-60
Main Authors: Wang, He Ping, Wang, Kai, Wang, Jing
Format: Article
Language:English
Subjects:
Asymptotic properties
Besov类
Eigenvalues
Entropy
Mathematical models
Mathematics
Mathematics and Statistics
Polynomials
Smoothness
Studies
Texts
Theorems
平滑
广义
渐近行为
熵
索伯列夫
订单
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Summary: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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-013-3044-9