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

Guadalupe, J. J.; Pérez, M.; Ruiz, F. J.; Varona, J. L.

doi:10.1090/S0002-9939-1992-1096211-0

Two notes on convergence and divergence a.e. of Fourier series with respect to some orthogonal systems
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by J. J. Guadalupe, M. Pérez, F. J. Ruiz and J. L. Varona PDF

Proc. Amer. Math. Soc. 116 (1992), 457-464 Request permission

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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