On the resolvents of dyadic paraproducts

Abstract

We consider the boundedness of certain singular integral operators that arose in the study of Sobolev spaces on Lipschitz curves, [P1]. The standard theory available (David and Journe's T1 Theorem, for instance; see [D]) does not apply to this case becuase the operators are not necessarily Calderon-Zygmund operators, [Ch]. One of these operators gives an explicit formula for the resolvent at ? = 1 of the dyadic paraproduct, [Ch].