Abstract
We study some problems related to convergence and divergence a.e. for Fourier series in systems { ϕ k } \{ {\phi _k}\} , where { ϕ k } \{ {\phi _k}\} is either a system of orthonormal polynomials with respect to a measure d μ d\mu on [ − 1 , 1 ] [-1,1] or a Bessel system on [ 0 , 1 ] [0,1] . We obtain boundedness in weighted L p {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 ] [-1,1] .
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