# Hokkaido Mathematical Journal

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

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### 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 42B20 commutator, fractional integral operator, the classical Morrey space, higher order commutator