Optimal Embeddings of Generalized Besov Spaces

Abstract

We prove optimal embeddings of generalized Besov spaces built-up over rearrangement invariant function spaces defined on Rⁿ with the Lebesgue measure into other rearrangement invariant spaces in the subcritical or critical cases and into generalized Hölder-Zygmund spaces in the supercritical case. The investigation is based on some real interpolation techniques and estimates of the rearrangement of f in terms of the modulus of continuity of f.