Suitable domains to define fractional integrals of Weyl via fractional powers of operators
Tom 202 / 2011
Studia Mathematica 202 (2011), 145-164
MSC: Primary 47A60, 26A33.
DOI: 10.4064/sm202-2-3
Streszczenie
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.
