Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series
Date
2019
Version
Acceso abierto / Sarbide irekia
Type
Artículo / Artikulua
Version
Versión aceptada / Onetsi den bertsioa
Project Identifier
MINECO//MTM2014-53009-P/ES/ 
MINECO//MTM2015-65888-C4-4-P/ES/
ES/1PE/MTM2016-76808-P
MINECO//MTM2015-65888-C4-4-P/ES/
ES/1PE/MTM2016-76808-P Impact
Abstract
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 fro ...
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Subject
Thresholding greedy algorithm,
Unconditional basis,
Quasi-greedy basis,
L-p-spaces,
Jacobi polynomials
Publisher
European Mathematical Society
Published in
Revista Matemática Iberoamericana, 2019, 35 (2), 561-574
Departament
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Publisher version
Sponsorship
The first two authors were partially supported by the Spanish Research Grant Analisis Vectorial, Multilineal y Aplicaciones, reference number MTM2014-53009-P, and the last two authors were partially supported by the Spanish Research Grant Ortogonalidad, Teoria de la Aproximacion y Aplicaciones en Fisica Matematica, reference number MTM2015-65888-C4-4-P. The first-named author also acknowledges the support of Spanish Research Grant Operators, lattices, and structure of Banach spaces, with reference MTM2016-76808-P.
