Entropy numbers of Besov classes of generalized smoothness on the sphere

Authors
Wang, He Ping Wang, Kai Wang, Jing
Citation
Wang, He Ping et al., Entropy numbers of Besov classes of generalized smoothness on the sphere, Acta mathematica Sinica. English series (Print) , 30(1), 2014, pp. 51-60
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
30
Issue
1
Year of publication
2014
Pages
51 - 60
Database
ACNP
SICI code
Abstract
We investigate the asymptotic behavior of the entropy numbers of Besov classes BB.p,.(Sd.1) of generalized smoothness on the sphere in Lq(Sd.1) for 1 . p, q, . . ., and get their asymptotic orders. We also obtain the exact orders of entropy numbers of Sobolev classes BWrp(Sd.1) in Lq(Sd.1) when p and/or q is equal to 1 or .. This provides the last piece as far as exact orders of entropy numbers of BWrp(Sd.1) in Lq(Sd.1) are concerned.