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arXiv · 2103.03016

Maximal characterisation of local Hardy spaces on locally doubling manifolds

Alessio Martini·Stefano Meda·Maria Vallarino
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Abstract

We prove a radial maximal function characterisation of the local atomic Hardy space h^1(M) on a Riemannian manifold M with positive injectivity radius and Ricci curvature bounded from below. As a consequence, we show that an integrable function belongs to h^1(M) if and only if either its local heat maximal function or its local Poisson maximal function are integrable. A key ingredient is a decomposition of H\"older cut-offs in terms of an appropriate class of approximations of the identity, which we obtain on arbitrary Ahlfors-regular metric measure spaces and generalises a previous result of A. Uchiyama.

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Alessio Martini, Stefano Meda, Maria Vallarino. 2021-03-04. Maximal characterisation of local Hardy spaces on locally doubling manifolds. https://doi.org/10.1007/s00209-021-02856-x

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