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...

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Detalles Bibliográficos
Autores: Albiac Alesanco, Fernando José, Ansorena, José L., Ciaurri, Óscar, Varona, Juan L.
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
Descripción
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.