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A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions

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A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions

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dc.contributor.author Fernández Vidal, Tomás es_ES
dc.contributor.author Galicer, Daniel es_ES
dc.contributor.author Sevilla Peris, Pablo es_ES
dc.date.accessioned 2023-07-03T18:01:26Z
dc.date.available 2023-07-03T18:01:26Z
dc.date.issued 2022-10 es_ES
dc.identifier.issn 1660-5446 es_ES
dc.identifier.uri http://hdl.handle.net/10251/194641
dc.description.abstract [EN] We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. Precisely, we show that any bounded sequence of holomorphic functions in some Hardy space, has a subsequence that converges uniformly over compact subsets to a function that also belongs to the same Hardy space. As a by-product of our results for spaces of functions on infinitely many variables, we also provide an elementary proof of a Montel-type theorem for the Hardy space of Dirichlet series. es_ES
dc.description.sponsorship Supported by PICT 2015-2299 and PICT 2018-0425. Daniel Galicer: Supported by CONICET-PIP 2014-2016 and PICT 2018-0425. Pablo Sevilla-Peris: Supported by MINECO and FEDER Project MTM2017-83262C2-1-P, GV Project AICO/2021/170 and MECD Grant PRX17/00040. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Mediterranean Journal of Mathematics es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Montel theorem es_ES
dc.subject Hardy spaces es_ES
dc.subject Infinite dimensional analysis es_ES
dc.subject Spaces of Dirichlet series es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00009-022-02110-6 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-1-P/ES/ANALISIS COMPLEJO Y GEOMETRIA EN ESPACIOS DE BANACH/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//AICO%2F2021%2F170//OPERADORES EN ESPACIOS DE FUNCIONES ANALITICAS O DIFERENCIABLES/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/ANPCyT//PICT 2015-2299/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/ANPCyT//PICT 2018-04250/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MECD//PRX17%2F00040/ es_ES
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 Fernández Vidal, T.; Galicer, D.; Sevilla Peris, P. (2022). A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions. Mediterranean Journal of Mathematics. 19(5):1-13. https://doi.org/10.1007/s00009-022-02110-6 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00009-022-02110-6 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 13 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 19 es_ES
dc.description.issue 5 es_ES
dc.relation.pasarela S\489477 es_ES
dc.contributor.funder GENERALITAT VALENCIANA es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder Ministerio de Educación, Cultura y Deporte es_ES
dc.contributor.funder Ministerio de Economía, Industria y Competitividad es_ES
dc.contributor.funder Agencia Nacional de Promoción Científica y Tecnológica, Argentina es_ES
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dc.description.references Defant, A., Domingo, G., Manuel, M., Pablo, S.-P.: Dirichlet Series and Holomorphic Functions in High Dimensions., Volume 37 of New Mathematical Monographs. Cambridge University Press, Cambridge (2019). https://doi.org/10.1017/9781108691611 es_ES
dc.description.references Defant, A., Maestre, M., Prengel, C.: Domains of convergence for monomial expansions of holomorphic functions in infinitely many variables. J. Reine Angew. Math. 634, 13–49 (2009). https://doi.org/10.1515/CRELLE.2009.068 es_ES
dc.description.references Defant, A., Schoolmann, I.: Variants of a theorem of Helson on general Dirichlet series. J. Funct. Anal. 279(5), 108569 (2020). https://doi.org/10.1016/j.jfa.2020.108569 es_ES
dc.description.references Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet Series, Volume 2 of Harish-Chandra Research Institute Lecture Notes. Hindustan Book Agency, New Delhi (2013) es_ES
dc.description.references Rudin, W.: Fourier Analysis on Groups, Interscience Tracts in Pure and Applied Mathematics. Interscience Publishers (a division of John Wiley and Sons), New York (1962) es_ES


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