Discrete Harmonic Analysis Associated with Jacobi Expansions
In this work we consider the operator associated with the three-term recurrence relation for the Jacobi polynomials and we study some classical operators in Harmonic Analysis in this context. Particularly, we are interested in the heat and Poisson semigroups and in the maximal operators related to t...
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Universidad de La Rioja (España)
2019
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oai-TES00000229282020-01-29Discrete Harmonic Analysis Associated with Jacobi ExpansionsLabarga Varona, EdgarIn this work we consider the operator associated with the three-term recurrence relation for the Jacobi polynomials and we study some classical operators in Harmonic Analysis in this context. Particularly, we are interested in the heat and Poisson semigroups and in the maximal operators related to them, in the Riesz transforms, and in the Littlewood-Paley-Stein g_k-functions. We obtain weighted l^p-inequalities for the heat and Poisson maximal operators and for the Riesz transforms when p>1 and the parameters of the Jacobi polynomials are greater than or equal to -1/2, and weighted weak inequalities in the case p=1 and the parameters greater than or equal to -1/2. We give weighted l^p-estimates for the g_k-functions when p>1 and the parameters are greater than or equal to -1/2. The method to prove these inequalities is based on the vector-valued Calderón-Zygmund theory in spaces of homogeneous type.Universidad de La Rioja (España)Ciaurri Ramírez, Óscar (null)Varona Malumbres, Juan Luis (null)2019text (thesis)application/pdfhttps://dialnet.unirioja.es/servlet/oaites?codigo=252732engLICENCIA 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 |
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eng |
| description |
In this work we consider the operator associated with the three-term recurrence relation for the Jacobi polynomials and we study some classical operators in Harmonic Analysis in this context. Particularly, we are interested in the heat and Poisson semigroups and in the maximal operators related to them, in the Riesz transforms, and in the Littlewood-Paley-Stein g_k-functions. We obtain weighted l^p-inequalities for the heat and Poisson maximal operators and for the Riesz transforms when p>1 and the parameters of the Jacobi polynomials are greater than or equal to -1/2, and weighted weak inequalities in the case p=1 and the parameters greater than or equal to -1/2. We give weighted l^p-estimates for the g_k-functions when p>1 and the parameters are greater than or equal to -1/2.
The method to prove these inequalities is based on the vector-valued Calderón-Zygmund theory in spaces of homogeneous type. |
| author2 |
Ciaurri Ramírez, Óscar (null) |
| author_facet |
Ciaurri Ramírez, Óscar (null) Labarga Varona, Edgar |
| format |
text (thesis) |
| author |
Labarga Varona, Edgar |
| spellingShingle |
Labarga Varona, Edgar Discrete Harmonic Analysis Associated with Jacobi Expansions |
| author_sort |
Labarga Varona, Edgar |
| title |
Discrete Harmonic Analysis Associated with Jacobi Expansions |
| title_short |
Discrete Harmonic Analysis Associated with Jacobi Expansions |
| title_full |
Discrete Harmonic Analysis Associated with Jacobi Expansions |
| title_fullStr |
Discrete Harmonic Analysis Associated with Jacobi Expansions |
| title_full_unstemmed |
Discrete Harmonic Analysis Associated with Jacobi Expansions |
| title_sort |
discrete harmonic analysis associated with jacobi expansions |
| publisher |
Universidad de La Rioja (España) |
| publishDate |
2019 |
| url |
https://dialnet.unirioja.es/servlet/oaites?codigo=252732 |
| work_keys_str_mv |
AT labargavaronaedgar discreteharmonicanalysisassociatedwithjacobiexpansions |
| _version_ |
1718346683975204864 |