We prove that $b$ is in $BMO(\R^n)$ if and only if the commutator $[b,I_{\alpha}]$ of the multiplication operator by
$b$ and the fractional integral operator $I_{\alpha}$ is bounded from the classical Morrey space $L^{p,\lambda}(\R^n)$ to $L^{q,\mu}(\R^n)$, where $1
Publié le : 2006-08-15
Classification:
commutator,
fractional integral operator,
the classical Morrey space,
higher order commutator,
42B25,
42B20
@article{1285766424,
author = {SHIRAI, Satoru},
title = {Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces},
journal = {Hokkaido Math. J.},
volume = {35},
number = {1},
year = {2006},
pages = { 683-696},
language = {en},
url = {http://dml.mathdoc.fr/item/1285766424}
}
SHIRAI, Satoru. Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces. Hokkaido Math. J., Tome 35 (2006) no. 1, pp. 683-696. http://gdmltest.u-ga.fr/item/1285766424/