A T(P) theorem for Zygmund spaces on domains

Abstract

Let D ⊂ R d be a bounded Lipschitz domain, ω be a modulus of continuity and let T be a convolution Calderón-Zygmund operator. We characterize the bounded restricted operators T D on the Zygmund space C ω (D). The characterization is based on properties of T D P for appropriate polynomials P restricted to D.