Entropy Numbers of Embeddings of Besov Spaces in Generalized Lipschitz Spaces

Abstract

We establish two-sided estimates for entropy numbers of embeddings between certain weighted Banach sequence spaces with mixed norms. These estimates are “almost” sharp, in the sense that upper and lower bounds differ only by logarithmic terms and improve previous results by D. E. Edmunds and D. Haroske (1999, Dissertationes Math. 380 , 1–43; 2000, J. Approx. Theory 104 , 226–271). As an application we obtain also new upper entropy estimates for embeddings of Besov spaces in generalized Lipschitz spaces.