Grand Morrey spaces and grand Hardy–Morrey spaces on Euclidean space

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Abstract

We define and study the grand Morrey spaces and the grand Hardy–Morrey spaces on Euclidean space. We also introduce the small block space and study the duality between the grand Morrey spaces and the small block spaces in order to extend the extrapolation theory to grand Morrey spaces. By using this extrapolation theory, we establish the boundedness of the Calderón–Zygmund operator, its linear and nonlinear commutators on grand Morrey spaces. We also obtain the boundedness of the Calderón–Zygmund operators and the parametric Marcinkiewicz integrals on the grand Hardy–Morrey spaces. Copyright © 2023 Mathematica Josephina, Inc.
Original languageEnglish
Article number180
JournalThe Journal of Geometric Analysis
Volume33
DOIs
Publication statusPublished - Mar 2023

Citation

Ho, K.-P. (2023). Grand Morrey spaces and grand Hardy–Morrey spaces on Euclidean space. The Journal of Geometric Analysis, 33. Retrieved from https://doi.org/10.1007/s12220-023-01229-6

Keywords

  • Grand Lebesgue spaces
  • Morrey spaces
  • Hardy spaces
  • Calderón–Zygmund operators
  • Commutators

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