Analysis of some injection bounds for Sobolev spaces by wavelet decomposition

We consider the Sobolev spaces Hs(?) and and the Besov spaces , where ? is a sufficiently regular (see Lemma 2) subdomain of R2. It is well known that for the values of s?[0,1/2) the two Sobolev spaces coincide, with equivalence of the norms, and that the inclusion holds. The Note is concerned with the explicit analysis of the constants appearing in the continuity bounds for the injections and and of their dependence on the regularity s of the spaces. The analysis is carried out by using the wavelet characterization of the corresponding norms.