Littlewood‐Paley characterization for Campanato spaces

The Littlewood-Paley characterization for the local approximation Campanato spaces Lpα is well known in the cases α≥0 and α=−np. We give in this paper a characterization of such a type for L2α spaces (and for Morrey-Campanato spaces L2,λ) for any α≥−n2. These spaces contain as spacial cases the well known spaces BMO of John and Nirenberg and its local version bmo