Solving dual integral equations on Lebesgue spaces

  1. Ciaurri, O. 2
  2. Guadalupe, J.J. 2
  3. Pérez, M. 1
  4. Varona, J.L. 2
  1. 1 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Revista:
Studia Mathematica

ISSN: 0039-3223

Ano de publicación: 2000

Volume: 142

Número: 3

Páxinas: 253-267

Tipo: Artigo

DOI: 10.4064/SM-142-3-253-267 SCOPUS: 2-s2.0-0012574021 WoS: WOS:000167585000005 GOOGLE SCHOLAR lock_openAcceso aberto editor

Outras publicacións en: Studia Mathematica

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Resumo

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 Lp 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 Σ∞n=0 cnJμ+2n+1 which converges in the Lp-norm and almost everywhere, where Jv denotes the Bessel function of order v. Finally, we study the uniqueness of the solution.