Real Interpolation of Generalized Besov-Hardy Spaces and Applications

Abstract

In this paper we consider generalized Hardy spaces which include classical Hardy spaces and Hardy-Lorentz spaces as special cases. We give real interpolation results for such spaces. As applications, we solve an interpolation problem for Besov spaces of generalized smoothness and prove the boundedness of pseudodifferential operators acting both in these spaces and in the local Hardy spaces. For the latter spaces, we also obtain wavelet decompositions.