Precise inclusion relations among Bergman-Besov and Bloch-Lipschitz spaces and H∞ on the unit ball of CN

Abstract

We describe exactly and fully which of the spaces of holomorphic functions in the title are included in which others. We provide either new results or new proofs. More importantly, we construct explicit functions in each space that show our relations are strict and the best possible. Many of our inclusions turn out to be sharper than the Sobolev imbeddings.