Solving dual integral equations on Lebesgue spaces
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1
Universidad de Zaragoza
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2
Universidad de La Rioja
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ISSN: 0039-3223
Year of publication: 2000
Volume: 142
Issue: 3
Pages: 253-267
Type: Article
More publications in: Studia Mathematica
Abstract
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 Lp 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 Σ∞n=0 cnJμ+2n+1 which converges in the Lp-norm and almost everywhere, where Jv denotes the Bessel function of order v. Finally, we study the uniqueness of the solution.