Singular integral operators on Lkp.Φ-spaces

Abstract

We extend singular integral operators T on L^p-spaces to operators on L^{p, φ}_k-spaces. The space L^{p, φ}_k is defined by using the mean oscillation and it is the space of classes of functions modulo \wp_k, polynomials of degree less than or equal to k. We define Tf for f \in L^{p, φ}_k as an element of L^p_loc/\wp_k with constructive method, and estimate the norm of Tf.