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Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri;  José Guadalupe;  Mario Pérez;  Juan Varona — 2000

Studia Mathematica

We study dual integral equations associated with Hankel transforms, that is, dual integral equations of Titchmarsh’s type. We reformulate these equations giving a better description in terms of continuous operators on L p spaces, and we solve them in these spaces. The solution is given both as an operator described in terms of integrals and as a series ∑ n = 0 ∞ c n J μ + 2 n + 1 which converges in the L p -norm and almost everywhere, where J ν denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution....

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

José J. Guadalupe;  Mario Pérez;  Francisco J. Ruiz;  Juan L. Varona — 1991

Publicacions Matemàtiques

Let w be a generalized Jacobi weight on the interval [-1,1] and, for each function f, let Sf 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 S in some weighted L spaces. The study of the norms of the kernels K related to the operators S allows us to obtain a relation between the Fourier series with respect to different generalized Jacobi weights.

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