Sharp Embeddings of Besov spaces involving small logarithmic smoothness

Abstract EN

We use Kolyada’s inequality and its converse form and the work ofAntónio M.

Caetano, Amiran Gogatishvili [17] to show sharp embedding's of Besov spaces (involving the zero classical smoothness and a logarithmic smoothness with the small exponent into Lorentz–Zygmund spaces.

We also determine the small growth envelopes of spaces In distinction to the case when the classical smoothness is positive, we show that we cannot describe all embedding's in question in terms of the small growth envelopes.