Applications of weighted estimates of Calderon's commutators

The paper introduces singular integral operators of a new type defined in the space L p with the weight function on the complex plane. For these operators, norm estimates are derived. Namely, if V is a complex-valued function on the complex plane satisfying the condition {pipe}V(z) - V(ζ){pipe} ≤ w{pipe}z - ζ{pipe} and F is an entire function, then we put, It is shown that if the weight function ω is a Muckenhoupt A p weight for 1 < p < ∞, then {pipe}{pipe}P * Ff{pipe}{pipe} p, ω ≤ C(F, w, p){pipe}{pipe}f{pipe}{pipe} p, ω. © 2012 Allerton Press, Inc.