Hokkaido Mathematical Journal

HO Kwok-Pun,

Atomic decompositions of weighted Hardy-Morrey spaces.

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




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(Secondary)42B30, 42B35
Uncontrolled KeywordsVector-valued maximal inequalities, Morrey-Hardy spaces, Atomic decompositions, Singular integral operator