COMPACT EMBEDDINGS OF BESOV SPACES IN EXPONENTIAL ORLICZ SPACES.

Let 1 < p < ∞, 0 < v < p′, let Ω be a bounded domain in Rn, and denote by idΩ the limiting compact embedding of the Besov space Bppn/p(Rn) into the exponential Orlicz space Lexp(tv)(Ω), mapping a function f onto its restriction f|Ω. In 1993 Triebel established, among others, two‐sided estimates for the entropy numbers of idΩ, 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. [ABSTRACT FROM PUBLISHER]