In this paper we consider a complete connected noncompact Riemannian manifold M with bounded geometry and spectral gap. We realize the dual space Y^h(M) of the Hardy-type space X^h(M), introduced in a previous paper of the authors, as the class of all locally square integrable functions satisfying suitable BMO-like conditions, where the role of the constants is played by the space of global k-quasi-harmonic functions. Furthermore we prove that Y^h(M) is also the dual of the space X^k_fin(M) of finite linear combination of X^k-atoms. As a consequence, if Z is a Banach space and T is a Z-valued linear operator defined on X^k_fin(M), then T extends to a bounded operator from X^k(M) to Z if and only if it is uniformly bounded on X^k-atoms. To obtain these results we prove the global solvability of the generalized Poisson equation L^ku=f with f in L^2_{loc}(M) and we study some properties of generalized Bergman spaces of harmonic functions on geodesic balls.
Harmonic Bergman spaces, the Poisson equation and the dual of Hardy-type spaces on certain noncompact manifolds / Mauceri, Giancarlo; Meda, Stefano; Vallarino, Maria. - In: ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA. CLASSE DI SCIENZE. - ISSN 0391-173X. - STAMPA. - 14:5(2015), pp. 1157-1188. [10.2422/2036-2145.201301_006]
Titolo: | Harmonic Bergman spaces, the Poisson equation and the dual of Hardy-type spaces on certain noncompact manifolds | |
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Data di pubblicazione: | 2015 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.2422/2036-2145.201301_006 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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maucerimedavallarino-AnnaliSNS.pdf | Articolo principale | 2. Post-print / Author's Accepted Manuscript | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
Abstract_F4_XIV_05.pdf | Articolo principale | 2a Post-print versione editoriale / Version of Record | Non Pubblico - Accesso privato/ristretto | Administrator Richiedi una copia |
http://hdl.handle.net/11583/2650256