Abstract

Given a bounded Lipschitz domain \(D\subset \mathbb{R}^d\), a higher-order modulus of continuity \(\omega\), and a convolution Calderón–Zygmund operator \(T\), the restricted operators \(T_D\) that are bounded on the Zygmund space \(\mathcal{C}_{\omega}(D)\) are described. The description is based on properties of the functions \(T_D P\) for appropriate polynomials \(P\) restricted to \(D\).

中文翻译：

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A $$T(P)$$ -域上齐格蒙德空间定理

摘要

给定一个有界 Lipschitz 域\(D\subset \mathbb{R}^d\)、一个高阶连续性模\(\omega\)和一个卷积 Calderón–Zygmund 算子\(T\)，受限算子描述了以 Zygmund 空间\(\mathcal{C}_{\omega}(D)\)为界的\(T_D\) 。该描述基于限制为\(D\)的适当多项式\(P\)的函数\(T_D P\)的属性。