Discrete Harmonic Analysis related to classical orthogonal polynomials

The present dissertation belongs to the so-called non-trigonometric discrete Harmonic Analysis, specifically to the one associated with classical orthogonal polynomials. Its aim is the study of the discrete analogues of some classical operators in Harmonic Analysis. To be specific, the convergence p...

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Autor principal:	Arenas Gómez, Alberto
Otros Autores:	Ciaurri Ramírez, Óscar (null)
Formato:	text (thesis)
Lenguaje:	eng
Publicado:	Universidad de La Rioja (España) 2019
Acceso en línea:	https://dialnet.unirioja.es/servlet/oaites?codigo=252734
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spelling	oai-TES00000229302020-01-29Discrete Harmonic Analysis related to classical orthogonal polynomialsArenas Gómez, AlbertoThe present dissertation belongs to the so-called non-trigonometric discrete Harmonic Analysis, specifically to the one associated with classical orthogonal polynomials. Its aim is the study of the discrete analogues of some classical operators in Harmonic Analysis. To be specific, the convergence problem of the multiplier of an interval for discrete Fourier series and the problem of the norm boundedness of the transplantation operator are studied. Regarding the first problem, the multiplier of an interval related to Jacobi polynomials is defined and sufficient conditions are given to ensure its norm boundedness with weights. If we consider no weights, a characterization is provided. Moreover, the characterization of the convergence is also given. Regarding the second problem, a transplantation theorem related to Jacobi coefficients is given when we consider weighted spaces. We prove that the transplantation operators are bounded in norm with weights by means of a semi-local Calderón- Zygmund theory which has been recently furnished. Moreover, some weighted weak estimates are provided. On its behalf, a transplantation theorem for Laguerre coefficients in weighted spaces is also given. In that case, we use a discrete local Calderón- Zygmund theory which is developed in the dissertation.Universidad de La Rioja (España)Ciaurri Ramírez, Óscar (null)2019text (thesis)application/pdfhttps://dialnet.unirioja.es/servlet/oaites?codigo=252734engLICENCIA DE USO: Los documentos a texto completo incluidos en Dialnet son de acceso libre y propiedad de sus autores y/o editores. Por tanto, cualquier acto de reproducción, distribución, comunicación pública y/o transformación total o parcial requiere el consentimiento expreso y escrito de aquéllos. Cualquier enlace al texto completo de estos documentos deberá hacerse a través de la URL oficial de éstos en Dialnet. Más información: https://dialnet.unirioja.es/info/derechosOAI \| INTELLECTUAL PROPERTY RIGHTS STATEMENT: Full text documents hosted by Dialnet are protected by copyright and/or related rights. This digital object is accessible without charge, but its use is subject to the licensing conditions set by its authors or editors. Unless expressly stated otherwise in the licensing conditions, you are free to linking, browsing, printing and making a copy for your own personal purposes. All other acts of reproduction and communication to the public are subject to the licensing conditions expressed by editors and authors and require consent from them. Any link to this document should be made using its official URL in Dialnet. More info: https://dialnet.unirioja.es/info/derechosOAI
institution	DialNet
collection	DialNet
language	eng
description	The present dissertation belongs to the so-called non-trigonometric discrete Harmonic Analysis, specifically to the one associated with classical orthogonal polynomials. Its aim is the study of the discrete analogues of some classical operators in Harmonic Analysis. To be specific, the convergence problem of the multiplier of an interval for discrete Fourier series and the problem of the norm boundedness of the transplantation operator are studied. Regarding the first problem, the multiplier of an interval related to Jacobi polynomials is defined and sufficient conditions are given to ensure its norm boundedness with weights. If we consider no weights, a characterization is provided. Moreover, the characterization of the convergence is also given. Regarding the second problem, a transplantation theorem related to Jacobi coefficients is given when we consider weighted spaces. We prove that the transplantation operators are bounded in norm with weights by means of a semi-local Calderón- Zygmund theory which has been recently furnished. Moreover, some weighted weak estimates are provided. On its behalf, a transplantation theorem for Laguerre coefficients in weighted spaces is also given. In that case, we use a discrete local Calderón- Zygmund theory which is developed in the dissertation.
author2	Ciaurri Ramírez, Óscar (null)
author_facet	Ciaurri Ramírez, Óscar (null) Arenas Gómez, Alberto
format	text (thesis)
author	Arenas Gómez, Alberto
spellingShingle	Arenas Gómez, Alberto Discrete Harmonic Analysis related to classical orthogonal polynomials
author_sort	Arenas Gómez, Alberto
title	Discrete Harmonic Analysis related to classical orthogonal polynomials
title_short	Discrete Harmonic Analysis related to classical orthogonal polynomials
title_full	Discrete Harmonic Analysis related to classical orthogonal polynomials
title_fullStr	Discrete Harmonic Analysis related to classical orthogonal polynomials
title_full_unstemmed	Discrete Harmonic Analysis related to classical orthogonal polynomials
title_sort	discrete harmonic analysis related to classical orthogonal polynomials
publisher	Universidad de La Rioja (España)
publishDate	2019
url	https://dialnet.unirioja.es/servlet/oaites?codigo=252734
work_keys_str_mv	AT arenasgomezalberto discreteharmonicanalysisrelatedtoclassicalorthogonalpolynomials
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Discrete Harmonic Analysis related to classical orthogonal polynomials

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