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arXiv · 1908.10057

A family of Hardy type spaces on nondoubling manifolds

Alessio Martini·Stefano Meda·Maria Vallarino
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Abstract

We introduce a decreasing one-parameter family $\mathfrak{X}^{\gamma}(M)$, $\gamma>0$, of Banach subspaces of the Hardy-Goldberg space $\mathfrak{h}^1(M)$ on certain nondoubling Riemannian manifolds with bounded geometry and we investigate their properties. In particular, we prove that $\mathfrak{X}^{1/2}(M)$ agrees with the space of all functions in $\mathfrak{h}^1(M)$ whose Riesz transform is in $L^1(M)$, and we obtain the surprising result that this space does not admit an atomic decomposition.

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Alessio Martini, Stefano Meda, Maria Vallarino. 2019-08-27. A family of Hardy type spaces on nondoubling manifolds. https://doi.org/10.1007/s10231-020-00956-9

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