Boundedness of the Hilbert Transform on Weighted Lorentz Spaces
[eng] The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedne...
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| Tipo de documento: | tese |
| Estado: | Versão publicada |
| Data de publicação: | 2012 |
| País: | España |
| Recursos: | Universidad de Barcelona |
| Repositório: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/42107 |
| Acesso em linha: | https://hdl.handle.net/2445/42107 http://hdl.handle.net/10803/108930 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Anàlisi harmònica Espais de Lorentz Espais de Hilbert Harmonic analysis Lorentz spaces Hilbert space |
| Resumo: | [eng] The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results extend and unify simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap, and the theory on classical Lorentz spaces Λp(w) and Ariño-Muckenhoupt weights Bp. |
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