We prove a radial maximal function characterisation of the local atomic Hardy space h1(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 h1(M) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder 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.

Maximal characterisation of local Hardy spaces on locally doubling manifolds / Martini, A.; Meda, S.; Vallarino, M.. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 300:(2022), pp. 1705-1739. [10.1007/s00209-021-02856-x]

Maximal characterisation of local Hardy spaces on locally doubling manifolds

Martini A.;Vallarino M.
2022

Abstract

We prove a radial maximal function characterisation of the local atomic Hardy space h1(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 h1(M) if and only if either its local heat maximal function or its local Poisson maximal function is integrable. A key ingredient is a decomposition of Hölder 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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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11583/2926192