J. Math. Anal. Appl. 322 (2006) 1215–1223 www.elsevier.com/locate/jmaa Two-weight norm inequalities for commutators of potential type integral operators Wenming Li College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, 050016, Hebei, PR China Received 25 January 2005 Available online 20 March 2006 Submitted by L. Grafakos Abstract We give a condition which is sufficient for the two-weight (p,q) inequalities for commutators of potential type integral operators. © 2005 Elsevier Inc. All rights reserved. Keywords: Potential type integral operator; Riesz potential; Commutator; Two-weight inequality 1. Introduction For a non-negative, locally integrable function Φ on R n , define the potential type operator T Φ by T Φ f(x) =  R n Φ(x − y)f(y)dy. Although the basic example is provided by the Riesz potentials or fractional integrals I α , defined by the kernel Φ(x) =|x | α−n ,0 <α<n, there are other important examples such as the Bessel potentials. They are denoted by J β,λ , β,λ> 0, and the kernel Φ(x) = K β,λ (x) is best defined by means of its Fourier transform  K β,λ (ξ) = (λ 2 +|ξ | 2 ) −β/2 . E-mail address: lwmingg@sina.com. 0022-247X/$ – see front matter © 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.jmaa.2005.08.051 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Elsevier - Publisher Connector