Solving dual integral equations on Lebesgue spaces

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 ${\displaystyle L^p}$ 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 ${\displaystyle {\sum }_{n=0}^{\infty }{c}_n{J}_{\mu +2n+1}}$ which converges in the ${\displaystyle L^p}$-norm and almost everywhere, where ${\displaystyle J_{\nu }}$ denotes the Bessel function of order ν. Finally, we study the uniqueness of the solution.