Solving dual integral equations on Lebesgue spaces
Volume 142 / 2000
Studia Mathematica 142 (2000), 253-267
DOI: 10.4064/sm-142-3-253-267
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 $L^p$ 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 $∑_{n=0}^{∞} c_n J_{μ+2n+1}$ 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.
