COMPACT EMBEDDINGS OF BESOV SPACES IN EXPONENTIAL ORLICZ SPACES

Let 1 < p <\infty, 0 < v < p^\prime , let \Omega be a bounded domain in R^n , and denote by rm id_ omega the limiting compact embedding of the Besov space B^{n/p}_{pp}(R^n) into the exponential Orlicz space L_{\exp (t^v)}(\Omega) , mapping a function f onto its restriction f\vert_Omega . In 1993 Triebel established, among others, two-sided estimates for the entropy numbers of rm id_omega , which are even asymptotically optimal for ‘small’ \nu . The aim of the paper is to improve the upper bounds in the case of ‘large’ \nu , where Triebelʹs estimates are not yet sharp, thus making a further step towards the conjectured correct asymptotic behaviour.