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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 language | English |
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Pages (from-to) | 2061-2085 |
Number of pages | 25 |
Journal | Annali di Matematica Pura ed Applicata |
Volume | 199 |
Issue number | 5 |
DOIs | |
Publication status | Published - 20 Feb 2020 |
Keywords
- Atom
- Exponential growth
- Hardy space
- Noncompact manifold
- Riesz transform
ASJC Scopus subject areas
- Applied Mathematics
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Dive into the research topics of 'A family of Hardy type spaces on nondoubling manifolds'. Together they form a unique fingerprint.Projects
- 1 Finished
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Sub-Elliptic Harmonic Analysis
Engineering & Physical Science Research Council
1/01/17 → 31/12/18
Project: Research Councils