### A note on Bessel function dual integral equation with weight function.

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Integral equations of the form (2) below, dual to (1) are studied from the point of view of finding their effective solutions, the results being given in Section 1. The results are applied in Section 2 for solving nonlocal problems for the polyharmonic functions in the half plane.

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