Besov Spaces with General Weights

Abstract

We introduce Besov spaces with general smoothness. These spaces unify and generalize the classical Besov spaces. We establish the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev embeddings. We establish the smooth atomic, molecular and wavelet decomposition of these function spaces. A characterization of these function spaces in terms of the difference relations is given.