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 2kL-k map X k(M) into L 1(T 2kM). © Mathematica Josephina, Inc. 2011.

Mauceri, G., Meda, S., Vallarino, M. (2012). Atomic Decomposition of Hardy Type Spaces on Certain Noncompact Manifolds. THE JOURNAL OF GEOMETRIC ANALYSIS, 22(3), 864-891 [10.1007/s12220-011-9218-8].

Atomic Decomposition of Hardy Type Spaces on Certain Noncompact Manifolds

MEDA, STEFANO
Secondo
;
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 2kL-k map X k(M) into L 1(T 2kM). © Mathematica Josephina, Inc. 2011.
Articolo in rivista - Articolo scientifico
Atomic Decomposition, Hardy-type Spaces, Noncompact Manifolds
English
2012
22
3
864
891
none
Mauceri, G., Meda, S., Vallarino, M. (2012). Atomic Decomposition of Hardy Type Spaces on Certain Noncompact Manifolds. THE JOURNAL OF GEOMETRIC ANALYSIS, 22(3), 864-891 [10.1007/s12220-011-9218-8].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/60435
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