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    Unconditional and quasi-greedy bases in L-p with applications to Jacobi polynomials Fourier series

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    2019060303_Albiac_UnconditionalQuasigreedy.pdf (342.7Kb)
    Date
    2019
    Author
    Albiac Alesanco, Fernando José Upna Orcid
    Ansorena, José L. 
    Ciaurri, Óscar 
    Varona, Juan L. 
    Version
    Acceso abierto / Sarbide irekia
    Type
    Artículo / Artikulua
    Version
    Versión aceptada / Onetsi den bertsioa
    Project Identifier
    MINECO//MTM2014-53009-P/ES/ openaire
    MINECO//MTM2015-65888-C4-4-P/ES/ openaire
    ES/1PE/MTM2016-76808-P 
    Impact
     
     
     
    10.4171/RMI/1062
     
     
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    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 ... [++]
    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. [--]
    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
    https://doi.org/10.4171/RMI/1062
    URI
    https://hdl.handle.net/2454/35946
    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.
    Appears in Collections
    • Artículos de revista - Aldizkari artikuluak [4926]
    • Artículos de revista DEIM - EIMS Aldizkari artikuluak [283]
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