Suitable domains to define fractional integrals of Weyl via fractional powers of operators

Volume 202 / 2011

Celso Martínez, Antonia Redondo, Miguel Sanz Studia Mathematica 202 (2011), 145-164 MSC: Primary 47A60, 26A33. DOI: 10.4064/sm202-2-3

Abstract

We present a new method to study the classical fractional integrals of Weyl. This new approach basically consists in considering these operators in the largest space where they make sense. In particular, we construct a theory of fractional integrals of Weyl by studying these operators in an appropriate Fréchet space. This is a function space which contains the $L^{p}( \mathbb{R})$-spaces, and it appears in a natural way if we wish to identify these fractional operators with fractional powers of a suitable non-negative operator. This identification allows us to give a unified view of the theory and provides some elegant proofs of some well-known results on the fractional integrals of Weyl.

Authors

  • Celso MartínezDepartament de Matemàtica Aplicada
    Universitat de València
    46100 Burjassot, València, Spain
    e-mail
  • Antonia RedondoDepartamento de Matemáticas
    I.E.S. Bachiller Sabuco
    02002 Albacete, Spain
    e-mail
  • Miguel SanzDepartament de Matemàtica Aplicada
    Universitat de València
    46100 Burjassot, València, Spain
    e-mail

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