$L^{p}$-integrability (1 ≤ p ≤ ∞) of a class of integral transforms

Yoshimitsu Hasegawa

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Solving dual integral equations on Lebesgue spaces

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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 $\sum_{n = 0}^{\infty} c_{n} J_{μ + 2 n + 1}$ 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...