A. V. Vasin, E. Doubtsov, “A <nobr>$T(P)$</nobr>-Theorem for Zygmund Spaces on Domains”, Mat. Zametki, 2023, Volume 114, Issue 1,Pages <nobr>38

This article is cited in 1 paper

A $T(P)$-Theorem for Zygmund Spaces on Domains

A. V. Vasin^a, E. Doubtsov^b

^a Admiral Makarov State University of Maritime and Inland Shipping, St. Petersburg
^b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Suppose 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 $D$.

Keywords: Zygmund space on a domain, $T(P)$-theorem, restricted Calderón–Zygmund operator.

UDC: 517.51+517.98

MSC: 42B20; 46E25

Received: 03.05.2022
Revised: 25.07.2022

DOI: 10.4213/mzm13575