Hokkaido Mathematical Journal

SHIRAI Satoru,

Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces.

Hokkaido Mathematical Journal, 35 (2006) pp.683-696

Fulltext

PDF

Abstract

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

MSC(Primary)42B25
MSC(Secondary)42B20
Uncontrolled Keywordscommutator, fractional integral operator, the classical Morrey space, higher order commutator