Two-Weight Inequalities for Commutators with Fractional Integral Operators Academic Article uri icon

abstract

  • In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $mu,lambdain A_{p,q}$ and $alpha/n+1/q=1/p$, the norm $| [b,I_alpha]:L^p(mu^p) o L^q(lambda^q) |$ is equivalent to the norm of $b$ in the weighted BMO space $BMO(
    u)$, where $
    u=mulambda^{-1}$. This work extends some of the results on this topic existing in the literature, and continues a line of investigation which was initiated by Bloom in 1985 and was recently developed further by the first author, Lacey, and Wick.

author list (cited authors)

  • Holmes, I., Rahm, R., & Spencer, S.

publication date

  • January 1, 2015 11:11 AM