A Note on Boundedness of Operators in Grand Grand Morrey Spaces

Conference paper
First Online:
Part of the Operator Theory: Advances and Applications book series (OT, volume 229)

Abstract

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calderón–Zygmund operators in the framework of grand grand Morrey spaces.

Keywords

Morrey spaces maximal operator Hardy-Littlewood maximal operator Calderón–Zygmund operator. 
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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Departamento de Matemática Centro CEAFInstituto Superior TécnicoLisboaPortugal
  2. 2.Departamento de MatemáticasPontificia Universidad JaverianaBogotáColombia

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