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, STEFANOSecondo
;
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.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
