Littlewood-Paley characterization for Campanato spaces

Abstract

The Littlewood-Paley characterization for the local approximation Campanato spacesLpαis well known in the casesα≥0andα=−np. We give in this paper a characterization of such a type forL2αspaces (and for Morrey-Campanato spacesL2,λ) for anyα≥−n2. These spaces contain as spacial cases the well known spaces BMO of John and Nirenberg and its local version bmo .