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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Two notes on convergence and divergence a.e. of Fourier series with respect to some orthogonal systems


Authors: J. J. Guadalupe, M. Pérez, F. J. Ruiz and J. L. Varona
Journal: Proc. Amer. Math. Soc. 116 (1992), 457-464
MSC: Primary 42C10; Secondary 33C10, 33C45, 42A20
MathSciNet review: 1096211
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Abstract: We study some problems related to convergence and divergence a.e. for Fourier series in systems $ \{ {\phi _k}\} $, where $ \{ {\phi _k}\} $ is either a system of orthonormal polynomials with respect to a measure $ d\mu $ on $ [-1,1]$ or a Bessel system on $ [0,1]$. We obtain boundedness in weighted $ {L^p}$ spaces for the maximal operators associated to Fourier-Jacobi and Fourier-Bessel series. On the other hand, we find general results about divergence a.e. of the Fourier series associated to Bessel systems and systems of orthonormal polynomials on $ [-1,1]$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1096211-0
PII: S 0002-9939(1992)1096211-0
Keywords: Fourier series, orthonormal polynomials, maximal operators, $ {A_p}$-weights
Article copyright: © Copyright 1992 American Mathematical Society