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.

Martini, A., Meda, S., Vallarino, M. (2022). Maximal characterisation of local Hardy spaces on locally doubling manifolds. MATHEMATISCHE ZEITSCHRIFT, 300(2), 1705-1739 [10.1007/s00209-021-02856-x].

Maximal characterisation of local Hardy spaces on locally doubling manifolds

Meda S.;
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.
Articolo in rivista - Articolo scientifico
Exponential growth; Hardy space; Locally doubling space; Maximal function; Riemannian manifold;
English
30-ago-2021
2022
300
2
1705
1739
open
Martini, A., Meda, S., Vallarino, M. (2022). Maximal characterisation of local Hardy spaces on locally doubling manifolds. MATHEMATISCHE ZEITSCHRIFT, 300(2), 1705-1739 [10.1007/s00209-021-02856-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/335909
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