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

• Autorzy: Celso Martínez , Antonia Redondo , Miguel Sanz
• Języki publikacji: EN

Abstrakty

EN

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 $L^{p}(ℝ)$-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.

Kategorie tematyczne

• 26A33: Fractional derivatives and integrals
• 47A60: Functional calculus

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2011
• Tom: 202
• Numer: 2
• Strony: 145-164

Daty

wydano

2011

Twórcy

autor

Celso Martínez

• Departament de Matemàtica Aplicada, Universitat de València, 46100 Burjassot, València, Spain

autor

Antonia Redondo

• Departamento de Matemáticas, I.E.S. Bachiller Sabuco, 02002 Albacete, Spain

autor

Miguel Sanz

• Departament de Matemàtica Aplicada, Universitat de València, 46100 Burjassot, València, Spain

Identyfikatory

DOI

10.4064/sm202-2-3