Two-microlocal Besov spaces and wavelets

Abstract

We give a characterization of the two-microlocal Besov spaces in terms of the local Besov type conditions. As an easy consequence, we obtain the inclusions between the two-microlocal Besov spaces and the local Besov spaces. These results are natural extensions of those obtained by Jaffard and Meyer, who treated the pointwise H\"older regularity in terms of two-microlocal estimates. The Daubechies wavelets play a key role throughout the paper.