## Illinois Journal of Mathematics

### A note on commutators of fractional integrals with ${\rm RBMO}(\mu)$ functions

#### Abstract

Let $\mu$ be a Borel measure on $\mathbb{R}^d$ which may be non-doubling. The only condition that $\mu$ must satisfy is $\mu(Q)\leq c_0l(Q)^n$ for any cube $Q\subset \mathbb{R}^d$ with sides parallel to the coordinate axes, for some fixed $n$ with $0 < n\leq d$. In this note we consider the commutators of fractional integrals with functions of the new BMO introduced by X. Tolsa.

#### Article information

Source
Illinois J. Math., Volume 46, Number 4 (2002), 1287-1298.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138480

Digital Object Identifier
doi:10.1215/ijm/1258138480

Mathematical Reviews number (MathSciNet)
MR1988264

Zentralblatt MATH identifier
1033.42008

#### Citation

Chen, Wengu; Sawyer, E. A note on commutators of fractional integrals with ${\rm RBMO}(\mu)$ functions. Illinois J. Math. 46 (2002), no. 4, 1287--1298. doi:10.1215/ijm/1258138480. https://projecteuclid.org/euclid.ijm/1258138480