Solving dual integral equations on Lebesgue spaces

Tom 142 / 2000

Óscar Ciaurri, José Guadalupe, Mario Pérez, Juan Varona Studia Mathematica 142 (2000), 253-267 DOI: 10.4064/sm-142-3-253-267


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.


  • Óscar Ciaurri
  • José Guadalupe
  • Mario Pérez
  • Juan Varona

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