Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces

The Bohr-Bohnenblust-Hille theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series ∑nann-s converges uniformly but not absolutely is less than or equal to 12, and this estimate is optimal. Equivalently, the supremum of the absolute convergence abscissas...

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Detalles Bibliográficos
Autor principal: Carando, Daniel German
Publicado: 2014
Materias:
Banach spaces
Vector-valued dirichlet series
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21575045_v7_n2_p513_Carando
http://hdl.handle.net/20.500.12110/paper_21575045_v7_n2_p513_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_21575045_v7_n2_p513_Carando
record_format dspace
spelling paper:paper_21575045_v7_n2_p513_Carando2023-06-08T16:34:24Z Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces Carando, Daniel German Banach spaces Vector-valued dirichlet series The Bohr-Bohnenblust-Hille theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series ∑nann-s converges uniformly but not absolutely is less than or equal to 12, and this estimate is optimal. Equivalently, the supremum of the absolute convergence abscissas of all Dirichlet series in the Hardy space H1 equals 1/2. By a surprising fact of Bayart the same result holds true if H1 is replaced by any Hardy space H∞, 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 < ∞. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21575045_v7_n2_p513_Carando http://hdl.handle.net/20.500.12110/paper_21575045_v7_n2_p513_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Banach spaces
Vector-valued dirichlet series
spellingShingle Banach spaces
Vector-valued dirichlet series
Carando, Daniel German
Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
topic_facet Banach spaces
Vector-valued dirichlet series
description The Bohr-Bohnenblust-Hille theorem states that the width of the strip in the complex plane on which an ordinary Dirichlet series ∑nann-s converges uniformly but not absolutely is less than or equal to 12, and this estimate is optimal. Equivalently, the supremum of the absolute convergence abscissas of all Dirichlet series in the Hardy space H1 equals 1/2. By a surprising fact of Bayart the same result holds true if H1 is replaced by any Hardy space H∞, 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 < ∞.
author Carando, Daniel German
author_facet Carando, Daniel German
author_sort Carando, Daniel German
title Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
title_short Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
title_full Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
title_fullStr Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
title_full_unstemmed Bohr's absolute convergence problem for Hp-Dirichlet series in banach spaces
title_sort bohr's absolute convergence problem for hp-dirichlet series in banach spaces
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_21575045_v7_n2_p513_Carando
http://hdl.handle.net/20.500.12110/paper_21575045_v7_n2_p513_Carando
work_keys_str_mv AT carandodanielgerman bohrsabsoluteconvergenceproblemforhpdirichletseriesinbanachspaces
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