Applications of Littlewood-Paley Theory for B˙σ-Morrey Spaces to the Boundedness of Integral Operators

Abstract

The boundedness of the various operators on B˙σ-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization of B˙σ-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization of B˙σ-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators on B˙σ-Lipschitz spaces is discussed.