# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 42 (2013) pp.131-157

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### Abstract

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.

MSC(Primary) 42B25 42B30, 42B35 Vector-valued maximal inequalities, Morrey-Hardy spaces, Atomic decompositions, Singular integral operator