Atomic decompositions of weighted Hardy-Morrey spaces

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20 Citations (Scopus)

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. Copyright © 2013 Hokkaido University, Department of Mathematics.
Original languageEnglish
Pages (from-to)131-157
JournalHokkaido Mathematical Journal
Volume42
Issue number1
DOIs
Publication statusPublished - 2013

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Atomic Decomposition
Morrey Space
Hardy Space
Littlewood-Paley Function
Weighted Lebesgue Spaces
Maximal Inequality
Singular Integral Operator
Boundedness
Decompose

Citation

Ho, K.-P. (2013). Atomic decompositions of weighted Hardy-Morrey spaces. Hokkaido Mathematical Journal, 42(1), 131-157.

Keywords

  • Vector-valued maximal inequalities
  • Morrey-Hardy spaces
  • Atomic decompositions
  • Singular integral operator