Multilinear operator-valued calderón-zygmund theory

We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing...

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Detalles Bibliográficos
Autores: Di Plinio, F., Li, K., Martikainen, H., Vuorinen, E.
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1213
Acceso en línea:http://hdl.handle.net/20.500.11824/1213
https://doi.org/10.1016/j.jfa.2020.108666
Access Level:acceso abierto
Palabra clave:Calderón–Zygmund operators
Operator-valued analysis
Multilinear analysis
UMD spaces
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spelling Multilinear operator-valued calderón-zygmund theoryDi Plinio, F.Li, K.Martikainen, H.Vuorinen, E.Calderón–Zygmund operatorsOperator-valued analysisMultilinear analysisUMD spacesWe develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing a suitable representation of mul- tilinear, operator-valued singular integrals in terms of operator-valued dyadic shifts and paraproducts, and studying the boundedness of these model operators via dyadic- probabilistic Banach space-valued analysis. In the bilinear case, we obtain a T(1)-type theorem without any additional assumptions on the Banach spaces other than the nec- essary UMD. Higher degrees of multilinearity are tackled via a new formulation of the Rademacher maximal function (RMF) condition. In addition to the natural UMD lat- tice cases, our RMF condition covers suitable tuples of non-commutative Lp-spaces. We employ our operator-valued theory to obtain new multilinear, multi-parameter, operator- valued theorems in the natural setting of UMD spaces with property α.202020202020info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1213https://doi.org/10.1016/j.jfa.2020.108666reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/abs/pii/S0022123620302093?via%3Dihubinfo:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/MINECO//MTM2017-82160-C2-1-Pinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/12132026-06-19T12:47:47Z
dc.title.none.fl_str_mv Multilinear operator-valued calderón-zygmund theory
title Multilinear operator-valued calderón-zygmund theory
spellingShingle Multilinear operator-valued calderón-zygmund theory
Di Plinio, F.
Calderón–Zygmund operators
Operator-valued analysis
Multilinear analysis
UMD spaces
title_short Multilinear operator-valued calderón-zygmund theory
title_full Multilinear operator-valued calderón-zygmund theory
title_fullStr Multilinear operator-valued calderón-zygmund theory
title_full_unstemmed Multilinear operator-valued calderón-zygmund theory
title_sort Multilinear operator-valued calderón-zygmund theory
dc.creator.none.fl_str_mv Di Plinio, F.
Li, K.
Martikainen, H.
Vuorinen, E.
author Di Plinio, F.
author_facet Di Plinio, F.
Li, K.
Martikainen, H.
Vuorinen, E.
author_role author
author2 Li, K.
Martikainen, H.
Vuorinen, E.
author2_role author
author
author
dc.subject.none.fl_str_mv Calderón–Zygmund operators
Operator-valued analysis
Multilinear analysis
UMD spaces
topic Calderón–Zygmund operators
Operator-valued analysis
Multilinear analysis
UMD spaces
description We develop a general theory of multilinear singular integrals with operator- valued kernels, acting on tuples of UMD Banach spaces. This, in particular, involves investigating multilinear variants of the R-boundedness condition naturally arising in operator-valued theory. We proceed by establishing a suitable representation of mul- tilinear, operator-valued singular integrals in terms of operator-valued dyadic shifts and paraproducts, and studying the boundedness of these model operators via dyadic- probabilistic Banach space-valued analysis. In the bilinear case, we obtain a T(1)-type theorem without any additional assumptions on the Banach spaces other than the nec- essary UMD. Higher degrees of multilinearity are tackled via a new formulation of the Rademacher maximal function (RMF) condition. In addition to the natural UMD lat- tice cases, our RMF condition covers suitable tuples of non-commutative Lp-spaces. We employ our operator-valued theory to obtain new multilinear, multi-parameter, operator- valued theorems in the natural setting of UMD spaces with property α.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1213
https://doi.org/10.1016/j.jfa.2020.108666
url http://hdl.handle.net/20.500.11824/1213
https://doi.org/10.1016/j.jfa.2020.108666
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/abs/pii/S0022123620302093?via%3Dihub
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/MINECO//MTM2017-82160-C2-1-P
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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