Archivio Istituzionale della RicercaIn this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the Hardy type spaces X^k(M), introduced in a previous paper of the authors, have an atomic characterization. An atom in X^k(M) is an atom in the Hardy space H 1(M) introduced by Carbonaro, Mauceri, and Meda, satisfying an “infinite dimensional” cancellation condition. As an application, we prove that the Riesz transforms of even order 2k map X^k(M) into L^1(T^2k(M)).
Atomic Decomposition of Hardy Type Spaces on Certain Noncompact Manifolds / Mauceri, G.; Meda, S.; Vallarino, Maria. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - STAMPA. - 22:3(2012), pp. 864-891. [10.1007/s12220-011-9218-8]
Atomic Decomposition of Hardy Type Spaces on Certain Noncompact Manifolds
VALLARINO, MARIA
2012
Abstract
In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We prove that the Hardy type spaces X^k(M), introduced in a previous paper of the authors, have an atomic characterization. An atom in X^k(M) is an atom in the Hardy space H 1(M) introduced by Carbonaro, Mauceri, and Meda, satisfying an “infinite dimensional” cancellation condition. As an application, we prove that the Riesz transforms of even order 2k map X^k(M) into L^1(T^2k(M)).
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https://hdl.handle.net/11583/2498434
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