Estimates for truncated area functionals on the Bloch space

Recently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n ≤ 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n = 6. We p...

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Detalles Bibliográficos
Autores: Efraimidis, Iason, Mas, Alejandro, Vukotic Jovsic, Dragan
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/710052
Acceso en línea:http://hdl.handle.net/10486/710052
https://dx.doi.org/10.1090/proc/16382
Access Level:acceso abierto
Palabra clave:Bloch Functions
Bloch Space
Coefficient Problems
Unit Disk
Coefficient
Matemáticas
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spelling Estimates for truncated area functionals on the Bloch spaceEfraimidis, IasonMas, AlejandroVukotic Jovsic, DraganBloch FunctionsBloch SpaceCoefficient ProblemsUnit DiskCoefficientMatemáticasRecently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n ≤ 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n = 6. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all n. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of 4/e). We also consider related weighted estimates for functionals involving the powers nt, t > 0, and show that the exponent t = 1 represents the critical case for the expected sharp estimateAll authors were partially supported by PID2019-106870GB-I00 from MICINN, Spain. The first author was supported by a María Zambrano contract, reference number CA3/RSUE/2021-00386, from UAM and Ministerio de Universidades, Spain (Plan de Recuperación, Transformación y Resiliencia)American Mathematical SocietyDepartamento de MatemáticasFacultad de Ciencias20222022-12-08research articlehttp://purl.org/coar/resource_type/c_2df8fbb1AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/710052https://dx.doi.org/10.1090/proc/16382reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7100522026-06-23T12:46:27Z
dc.title.none.fl_str_mv Estimates for truncated area functionals on the Bloch space
title Estimates for truncated area functionals on the Bloch space
spellingShingle Estimates for truncated area functionals on the Bloch space
Efraimidis, Iason
Bloch Functions
Bloch Space
Coefficient Problems
Unit Disk
Coefficient
Matemáticas
title_short Estimates for truncated area functionals on the Bloch space
title_full Estimates for truncated area functionals on the Bloch space
title_fullStr Estimates for truncated area functionals on the Bloch space
title_full_unstemmed Estimates for truncated area functionals on the Bloch space
title_sort Estimates for truncated area functionals on the Bloch space
dc.creator.none.fl_str_mv Efraimidis, Iason
Mas, Alejandro
Vukotic Jovsic, Dragan
author Efraimidis, Iason
author_facet Efraimidis, Iason
Mas, Alejandro
Vukotic Jovsic, Dragan
author_role author
author2 Mas, Alejandro
Vukotic Jovsic, Dragan
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Bloch Functions
Bloch Space
Coefficient Problems
Unit Disk
Coefficient
Matemáticas
topic Bloch Functions
Bloch Space
Coefficient Problems
Unit Disk
Coefficient
Matemáticas
description Recently, Kayumov [Lobachevskii J. Math. 38 (2017), pp. 466–468] obtained a sharp estimate for the n-th truncated area functional for normalized functions in the Bloch space for n ≤ 5 and then, together with Wirths [Lobachevskii J. Math. 40 (2019), pp. 1319–1323], extended the result for n = 6. We prove that for the functions with non-negative Taylor coefficients, the same sharp estimate is valid for all n. For arbitrary functions, we obtain an estimate that is asymptotically of the same order but slightly larger (roughly by a factor of 4/e). We also consider related weighted estimates for functionals involving the powers nt, t > 0, and show that the exponent t = 1 represents the critical case for the expected sharp estimate
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-12-08
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/710052
https://dx.doi.org/10.1090/proc/16382
url http://hdl.handle.net/10486/710052
https://dx.doi.org/10.1090/proc/16382
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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