On conditions for the boundedness of the Weyl fractional integral on weighted $L^p$ spaces

De Rosa, Liliana, and de la Torre, Alberto. "On conditions for the boundedness of the Weyl fractional integral on weighted $L^p$ spaces." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 17-36. <http://eudml.org/doc/249339>.

@article{DeRosa2004,
abstract = {In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_\{\alpha \}^+$ from $L^p(v)$ into $L^p(w)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p: 1 \le p < \infty $ there exist non-trivial weights $w$ such that $I_\{\alpha \}^+$ is bounded from $L^p(w)$ into itself, even in the case $\alpha > 1$.},
author = {De Rosa, Liliana, de la Torre, Alberto},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Weyl fractional integrals; weights; weights},
language = {eng},
number = {1},
pages = {17-36},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On conditions for the boundedness of the Weyl fractional integral on weighted $L^p$ spaces},
url = {http://eudml.org/doc/249339},
volume = {45},
year = {2004},
}

TY - JOUR
AU - De Rosa, Liliana
AU - de la Torre, Alberto
TI - On conditions for the boundedness of the Weyl fractional integral on weighted $L^p$ spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 17
EP - 36
AB - In this paper we give a sufficient condition on the pair of weights $(w,v)$ for the boundedness of the Weyl fractional integral $I_{\alpha }^+$ from $L^p(v)$ into $L^p(w)$. Under some restrictions on $w$ and $v$, this condition is also necessary. Besides, it allows us to show that for any $p: 1 \le p < \infty $ there exist non-trivial weights $w$ such that $I_{\alpha }^+$ is bounded from $L^p(w)$ into itself, even in the case $\alpha > 1$.
LA - eng
KW - Weyl fractional integrals; weights; weights
UR - http://eudml.org/doc/249339
ER -