Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we show that no normalized unconditional basis in L-p, p not equal 2, can be semi-n...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/35946 |
| Acceso en línea: | https://hdl.handle.net/2454/35946 |
| Access Level: | acceso abierto |
| Palabra clave: | Thresholding greedy algorithm Unconditional basis Quasi-greedy basis L-p-spaces Jacobi polynomials |
| Sumario: | We show that the decreasing rearrangement of the Fourier series with respect to the Jacobi polynomials for functions in L-p does not converge unless p = 2. As a by-product of our work on quasi-greedy bases in L-p(µ), we show that no normalized unconditional basis in L-p, p not equal 2, can be semi-normalized in L-q for q not equal p, thus extending a classical theorem of Kadets and Pelczynski from 1968. |
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