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Compact Embeddings of Besov Spaces in Exponential Orlicz Spaces
Author(s) -
Kühn Thomas
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702003848
Subject(s) - mathematics , embedding , bounded function , limiting , besov space , exponential function , space (punctuation) , pure mathematics , function (biology) , function space , domain (mathematical analysis) , entropy (arrow of time) , exponential growth , mathematical analysis , interpolation space , computer science , functional analysis , physics , biochemistry , chemistry , gene , mechanical engineering , quantum mechanics , artificial intelligence , evolutionary biology , biology , engineering , operating system
Let 1 < p < ∞, 0 < v < p ′, let Ω be a bounded domain in R n , and denote by id Ω the limiting compact embedding of the Besov spaceB p pn / p(R n ) into the exponential Orlicz space L exp ( t v )(Ω), mapping a function f onto its restriction f | Ω . In 1993 Triebel established, among others, two‐sided estimates for the entropy numbers of id Ω , which are even asymptotically optimal for ‘small’ ν. The aim of the paper is to improve the upper bounds in the case of ‘large’ ν, where Triebel's estimates are not yet sharp, thus making a further step towards the conjectured correct asymptotic behaviour.