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arXiv · 2205.06211

A T(P) theorem for Zygmund spaces on domains

Andrei V. Vasin·Evgueni Doubtsov
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Abstract

Let $D\subset \mathbb{R}^d$ be a bounded Lipschitz domain, $\omega$ be a high order modulus of continuity and let $T$ be a convolution Calder\'{o}n-Zygmund operator. We characterize the bounded restricted operators $T_D$ on the Zygmund space $\mathcal{C}_{\omega}(D)$. The characterization is based on properties of $T_D P$ for appropriate polynomials $P$ restricted to $D$.

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Andrei V. Vasin, Evgueni Doubtsov. 2022-05-12. A T(P) theorem for Zygmund spaces on domains. https://arxiv.org/abs/2205.06211

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