Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions

We investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight m...

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Authors: Ciaurri, O. [0000-0002-1695-3311], Nowak, A., Roncal, L. [0000-0003-0852-3677]
Format: article
Status:Published version
Publication Date:2017
Country:España
Institution:Universidad de La Rioja (UR)
Repository:RIUR. Repositorio Institucional de la Universidad de La Rioja
OAI Identifier:oai:portal.dialnet.es:doc/5bbc68dab750603269e810cf
Online Access:https://investigacion.unirioja.es/documentos/5bbc68dab750603269e810cf
Access Level:Open access
Keyword:Axially symmetric solution
Euler{ poisson{darboux equation
Hankel transform
Kernel estimate
Legendre function
Mixed norm estimate
Radial function
Spherical mean
Spherical radon transform
Strichartz estimate
Two-weight estimate
Wave equation
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spelling Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functionsCiaurri, O. [0000-0002-1695-3311]Nowak, A.Roncal, L. [0000-0003-0852-3677]Axially symmetric solutionEuler{ poisson{darboux equationHankel transformKernel estimateLegendre functionMixed norm estimateRadial functionSpherical meanSpherical radon transformStrichartz estimateTwo-weight estimateWave equationWe investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz-Type estimates for solutions to certain Cauchy problems for classical Euler{Poisson{Darboux and wave equations with radial initial data. © 2017 Society for Industrial and Applied Mathematics.2017info:eu-repo/semantics/articleSubtype: Articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://investigacion.unirioja.es/documentos/5bbc68dab750603269e810cfreponame:RIUR. Repositorio Institucional de la Universidad de La Riojainstname:Universidad de La Rioja (UR)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1137/17M1117756info:eu-repo/semantics/altIdentifier/wos/WOS:000418671600003info:eu-repo/semantics/altIdentifier/pissn/0036-1410Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions, 2017, vol. 49, núm. 6, pág. 4402-4439info:eu-repo/semantics/openAccessoai:portal.dialnet.es:doc/5bbc68dab750603269e810cf2026-06-14T12:47:17Z
dc.title.none.fl_str_mv Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
title Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
spellingShingle Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
Ciaurri, O. [0000-0002-1695-3311]
Axially symmetric solution
Euler{ poisson{darboux equation
Hankel transform
Kernel estimate
Legendre function
Mixed norm estimate
Radial function
Spherical mean
Spherical radon transform
Strichartz estimate
Two-weight estimate
Wave equation
title_short Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
title_full Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
title_fullStr Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
title_full_unstemmed Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
title_sort Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions
dc.creator.none.fl_str_mv Ciaurri, O. [0000-0002-1695-3311]
Nowak, A.
Roncal, L. [0000-0003-0852-3677]
author Ciaurri, O. [0000-0002-1695-3311]
author_facet Ciaurri, O. [0000-0002-1695-3311]
Nowak, A.
Roncal, L. [0000-0003-0852-3677]
author_role author
author2 Nowak, A.
Roncal, L. [0000-0003-0852-3677]
author2_role author
author
dc.subject.none.fl_str_mv Axially symmetric solution
Euler{ poisson{darboux equation
Hankel transform
Kernel estimate
Legendre function
Mixed norm estimate
Radial function
Spherical mean
Spherical radon transform
Strichartz estimate
Two-weight estimate
Wave equation
topic Axially symmetric solution
Euler{ poisson{darboux equation
Hankel transform
Kernel estimate
Legendre function
Mixed norm estimate
Radial function
Spherical mean
Spherical radon transform
Strichartz estimate
Two-weight estimate
Wave equation
description We investigate a generalized spherical means operator, in other words the generalized spherical mean Radon transform, acting on radial functions. We establish an integral representation of this operator and find precise estimates of the corresponding kernel. As the main result, we prove two-weight mixed norm estimates for the integral operator, with general power weights involved. This leads to weighted Strichartz-Type estimates for solutions to certain Cauchy problems for classical Euler{Poisson{Darboux and wave equations with radial initial data. © 2017 Society for Industrial and Applied Mathematics.
publishDate 2017
dc.date.none.fl_str_mv 2017
dc.type.none.fl_str_mv info:eu-repo/semantics/article
Subtype: Article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://investigacion.unirioja.es/documentos/5bbc68dab750603269e810cf
url https://investigacion.unirioja.es/documentos/5bbc68dab750603269e810cf
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1137/17M1117756
info:eu-repo/semantics/altIdentifier/wos/WOS:000418671600003
info:eu-repo/semantics/altIdentifier/pissn/0036-1410
Two-weight mixed norm estimates for a generalized spherical mean radon transform acting on radial functions, 2017, vol. 49, núm. 6, pág. 4402-4439
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:RIUR. Repositorio Institucional de la Universidad de La Rioja
instname:Universidad de La Rioja (UR)
instname_str Universidad de La Rioja (UR)
reponame_str RIUR. Repositorio Institucional de la Universidad de La Rioja
collection RIUR. Repositorio Institucional de la Universidad de La Rioja
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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