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

Celso Martínez, Antonia Redondo, and Miguel Sanz. "Suitable domains to define fractional integrals of Weyl via fractional powers of operators." Studia Mathematica 202.2 (2011): 145-164. <http://eudml.org/doc/285840>.

@article{CelsoMartínez2011,
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 $L^\{p\}(ℝ)$-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.},
author = {Celso Martínez, Antonia Redondo, Miguel Sanz},
journal = {Studia Mathematica},
language = {eng},
number = {2},
pages = {145-164},
title = {Suitable domains to define fractional integrals of Weyl via fractional powers of operators},
url = {http://eudml.org/doc/285840},
volume = {202},
year = {2011},
}

TY - JOUR
AU - Celso Martínez
AU - Antonia Redondo
AU - Miguel Sanz
TI - Suitable domains to define fractional integrals of Weyl via fractional powers of operators
JO - Studia Mathematica
PY - 2011
VL - 202
IS - 2
SP - 145
EP - 164
AB - 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.
LA - eng
UR - http://eudml.org/doc/285840
ER -