A family of Hardy type spaces on nondoubling manifolds

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  • University of Milano-Bicocca, Piazza dell'Ateneo Nuovo, 1, 20126 Milano, Italy.
  • Politecnico di Torino


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
JournalAnnali di Matematica Pura ed Applicata
Publication statusPublished - 20 Feb 2020


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

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