A T(P) theorem for Zygmund spaces on domains

2022/05/12 by Vasin, Andrei V., Doubtsov, Evgueni
#42B20 #46E25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2205.06211

Abstract

Let D⊂ ℝ^d be a bounded Lipschitz domain, ω be a high order 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.

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