A family of Hardy type spaces on nondoubling manifolds

Alessio Martini, Stefano Meda, Maria Vallarino

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Abstract

We introduce a decreasing one-parameter family X γ(M) , γ> 0 , of Banach subspaces of the Hardy–Goldberg space h 1(M) on certain nondoubling Riemannian manifolds with bounded geometry, and we investigate their properties. In particular, we prove that X 1 / 2(M) agrees with the space of all functions in h 1(M) whose Riesz transform is in L 1(M) , and we obtain the surprising result that this space does not admit an atomic decomposition.

Original languageEnglish
Pages (from-to)2061-2085
Number of pages25
JournalAnnali di Matematica Pura ed Applicata
Volume199
Issue number5
DOIs
Publication statusPublished - 20 Feb 2020

Keywords

  • Atom
  • Exponential growth
  • Hardy space
  • Noncompact manifold
  • Riesz transform

ASJC Scopus subject areas

  • Applied Mathematics

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