A family of Hardy type spaces on nondoubling manifolds
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Colleges, School and Institutes
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.
|Number of pages||25|
|Journal||Annali di Matematica Pura ed Applicata|
|Publication status||Published - 20 Feb 2020|
- Atom, Exponential growth, Hardy space, Noncompact manifold, Riesz transform