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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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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

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Título: A Montel-Type Theorem for Hardy Spaces of Holomorphic Functions
Autor: Fernández Vidal, Tomás Galicer, Daniel Sevilla Peris, Pablo
Entidad UPV: Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural
Fecha difusión:
Resumen:
[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 ...[+]
Palabras clave: Montel theorem , Hardy spaces , Infinite dimensional analysis , Spaces of Dirichlet series
Derechos de uso: Reserva de todos los derechos
Fuente:
Mediterranean Journal of Mathematics. (issn: 1660-5446 )
DOI: 10.1007/s00009-022-02110-6
Editorial:
Springer-Verlag
Versión del editor: https://doi.org/10.1007/s00009-022-02110-6
Código del Proyecto:
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/
info:eu-repo/grantAgreement/GENERALITAT VALENCIANA//AICO%2F2021%2F170//OPERADORES EN ESPACIOS DE FUNCIONES ANALITICAS O DIFERENCIABLES/
info:eu-repo/grantAgreement/ANPCyT//PICT 2015-2299/
info:eu-repo/grantAgreement/ANPCyT//PICT 2018-04250/
info:eu-repo/grantAgreement/MECD//PRX17%2F00040/
Agradecimientos:
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 ...[+]
Tipo: Artículo

References

Aleman, A., Olsen, J.-F., Saksman, E.: Fourier multipliers for Hardy spaces of Dirichlet series. Int. Math. Res. Not. IMRN 16, 4368–4378 (2014). https://doi.org/10.1093/imrn/rnt080

Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math. 136(3), 203–236 (2002). https://doi.org/10.1007/s00605-002-0470-7

Bayart, F.: Personal comunication (2019) [+]
Aleman, A., Olsen, J.-F., Saksman, E.: Fourier multipliers for Hardy spaces of Dirichlet series. Int. Math. Res. Not. IMRN 16, 4368–4378 (2014). https://doi.org/10.1093/imrn/rnt080

Bayart, F.: Hardy spaces of Dirichlet series and their composition operators. Monatsh. Math. 136(3), 203–236 (2002). https://doi.org/10.1007/s00605-002-0470-7

Bayart, F.: Personal comunication (2019)

Bayart, F., Defant, A., Frerick, L., Maestre, M., Sevilla-Peris, P.M.: Multipliers of Dirichlet series and monomial series expansions of holomorphic functions in infinitely many variables. Math. Ann. 138(1–2), 837–876 (2017). https://doi.org/10.1007/s00208-016-1511-1

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Conway, J.B.: Functions of One Complex Variable. II, Volume 159 of Graduate Texts in Mathematics. Springer, New York (1995). https://doi.org/10.1007/978-1-4612-0817-4

Defant, A., Fernández Vidal, T., Schoolmann, I., Sevilla-Peris, P.: Fréchet spaces of general Dirichlet series. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 115(3), Paper No. 138, 34 (2021). https://doi.org/10.1007/s13398-021-01074-8

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

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

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

Queffélec, H., Queffélec, M.: Diophantine Approximation and Dirichlet Series, Volume 2 of Harish-Chandra Research Institute Lecture Notes. Hindustan Book Agency, New Delhi (2013)

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)

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