Lp-BOUNDEDNESS OF THE GENERAL INDEX TRANSFORMS

نویسندگان

  • Semyon B. Yakubovich
  • SEMYON B. YAKUBOVICH
چکیده

Abstract We establish the boundedness properties in Lp for a class of integral transformations with respect to an index of hypergeometric functions. In particular, by using the RieszThorin interpolation theorem we get the corresponding results in Lp(R+), 1 ≤ p ≤ 2 for the Kontorovich-Lebedev, Mehler-Fock and Olevskii index transforms. An inversion theorem is proved for general index transformation. The case p = 2 is known as the Plancherel type theory for this class of transformations.

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تاریخ انتشار 2004