We obtain the Fefferman-Stein vector-valued maximal inequalities on Morrey spaces generated by weighted Lebesgue spaces. Using these inequalities, we introduce and define the weighted Hardy-Morrey spaces by using the Littlewood-Paley functions. We also establish the non-smooth atomic decompositions for the weighted Hardy-Morrey spaces and, as an application of the decompositions, we obtain the boundedness of a class of singular integral operators on the weighted Hardy-Morrey spaces. Copyright © 2013 Hokkaido University, Department of Mathematics.
CitationHo, K.-P. (2013). Atomic decompositions of weighted Hardy-Morrey spaces. Hokkaido Mathematical Journal, 42(1), 131-157.
- Vector-valued maximal inequalities
- Morrey-Hardy spaces
- Atomic decompositions
- Singular integral operator