Archivio Istituzionale della RicercaWe introduce a decreasing one-parameter family Xγ(M) , γ> 0 , of Banach subspaces of the Hardy–Goldberg space h1(M) on certain nondoubling Riemannian manifolds with bounded geometry, and we investigate their properties. In particular, we prove that X1 / 2(M) agrees with the space of all functions in h1(M) whose Riesz transform is in L1(M) , and we obtain the surprising result that this space does not admit an atomic decomposition.
A family of Hardy-type spaces on nondoubling manifolds / Martini, A.; Meda, S.; Vallarino, M.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 199:5(2020), pp. 2061-2085. [10.1007/s10231-020-00956-9]
A family of Hardy-type spaces on nondoubling manifolds
Martini A.;Vallarino M.
2020
Abstract
We introduce a decreasing one-parameter family Xγ(M) , γ> 0 , of Banach subspaces of the Hardy–Goldberg space h1(M) on certain nondoubling Riemannian manifolds with bounded geometry, and we investigate their properties. In particular, we prove that X1 / 2(M) agrees with the space of all functions in h1(M) whose Riesz transform is in L1(M) , and we obtain the surprising result that this space does not admit an atomic decomposition.
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math.FA.pdf
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https://hdl.handle.net/11583/2858147