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.
Martini, A., Meda, S., Vallarino, M. (2020). A family of Hardy-type spaces on nondoubling manifolds. ANNALI DI MATEMATICA PURA ED APPLICATA, 199(5), 2061-2085 [10.1007/s10231-020-00956-9].
A family of Hardy-type spaces on nondoubling manifolds
Meda S.;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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
