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BOHR'S ABSOLUTE CONVERGENCE PROBLEM FOR Hp-DIRICHLET SERIES IN BANACH SPACES

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BOHR'S ABSOLUTE CONVERGENCE PROBLEM FOR Hp-DIRICHLET SERIES IN BANACH SPACES

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dc.contributor.author Carando, Daniel es_ES
dc.contributor.author Defant, Andreas es_ES
dc.contributor.author Sevilla Peris, Pablo es_ES
dc.date.accessioned 2016-12-01T08:45:55Z
dc.date.available 2016-12-01T08:45:55Z
dc.date.issued 2014
dc.identifier.issn 2157-5045
dc.identifier.uri http://hdl.handle.net/10251/74826
dc.description PUBLISHED BY mathematical sciences publishers nonprofit scientific publishing http://msp.org/ © 2014 Mathematical Sciences Publishers es_ES
dc.description.abstract [EN] The Bohr–Bohnenblust–Hille theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series P n ann −s converges uniformly but not absolutely is less than or equal to 1 2 , and this estimate is optimal. Equivalently, the supremum of the absolute convergence abscissas of all Dirichlet series in the Hardy space H∞ equals 1 2 . By a surprising fact of Bayart the same result holds true if H∞ is replaced by any Hardy space Hp, 1 ≤ p < ∞, of Dirichlet series. For Dirichlet series with coefficients in a Banach space X the maximal width of Bohr’s strips depend on the geometry of X; Defant, García, Maestre and Pérez-García proved that such maximal width equals 1 − 1/Cot X, where Cot X denotes the maximal cotype of X. Equivalently, the supremum over the absolute convergence abscissas of all Dirichlet series in the vector-valued Hardy space H∞(X) equals 1 − 1/Cot X. In this article we show that this result remains true if H∞(X) is replaced by the larger class Hp(X), 1 ≤ p < ∞ es_ES
dc.description.sponsorship Carando was partially supported by CONICET PIP 0624, PICT 2011-1456 and UBACyT 1-746. Defant and Sevilla-Peris were supported by MICINN project MTM2011-22417. Sevilla-Peris was partially supported by UPV-SP20120700. en_EN
dc.language Inglés es_ES
dc.publisher Mathematical Sciences Publishers (MSP) es_ES
dc.relation CONICET PIP 0624 PICT 2011-1456 UBACyT 1-746 es_ES
dc.relation MICINN MTM2011-22417 es_ES
dc.relation UPV-SP20120700 es_ES
dc.relation.ispartof Analysis and PDE es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Vector-valued Dirichlet series es_ES
dc.subject Vector-valued H-p spaces es_ES
dc.subject Banach spaces es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title BOHR'S ABSOLUTE CONVERGENCE PROBLEM FOR Hp-DIRICHLET SERIES IN BANACH SPACES es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.2140/apde.2014.7.513
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural es_ES
dc.description.bibliographicCitation Carando, D.; Defant, A.; Sevilla Peris, P. (2014). BOHR'S ABSOLUTE CONVERGENCE PROBLEM FOR Hp-DIRICHLET SERIES IN BANACH SPACES. Analysis and PDE. 7(2):513-527. doi:10.2140/apde.2014.7.513 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion https://dx.doi.org/10.2140/apde.2014.7.513 es_ES
dc.description.upvformatpinicio 513 es_ES
dc.description.upvformatpfin 527 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 7 es_ES
dc.description.issue 2 es_ES
dc.relation.senia 286440 es_ES
dc.identifier.eissn 1948-206X


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