Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights.

José J. Guadalupe; Mario Pérez; Francisco J. Ruiz; Juan L. Varona

Publicacions Matemàtiques (1991)

  • Volume: 35, Issue: 2, page 449-459
  • ISSN: 0214-1493

Abstract

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Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

How to cite

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Guadalupe, José J., et al. "Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights.." Publicacions Matemàtiques 35.2 (1991): 449-459. <http://eudml.org/doc/41701>.

@article{Guadalupe1991,
abstract = {Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.},
author = {Guadalupe, José J., Pérez, Mario, Ruiz, Francisco J., Varona, Juan L.},
journal = {Publicacions Matemàtiques},
keywords = {generalized Jacobi weight; Fourier series; orthogonal polynomials; weighted spaces; uniform boundedness},
language = {eng},
number = {2},
pages = {449-459},
title = {Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights.},
url = {http://eudml.org/doc/41701},
volume = {35},
year = {1991},
}

TY - JOUR
AU - Guadalupe, José J.
AU - Pérez, Mario
AU - Ruiz, Francisco J.
AU - Varona, Juan L.
TI - Weighted Lp boundedness of Fourier series with respect to generalized Jacobi weights.
JO - Publicacions Matemàtiques
PY - 1991
VL - 35
IS - 2
SP - 449
EP - 459
AB - Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Snf denote the n-th partial sum of the Fourier series of f in the orthogonal polynomials associated to w. We prove a result about uniform boundedness of the operators Sn in some weighted Lp spaces. The study of the norms of the kernels Kn related to the operators Sn allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.
LA - eng
KW - generalized Jacobi weight; Fourier series; orthogonal polynomials; weighted spaces; uniform boundedness
UR - http://eudml.org/doc/41701
ER -

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