Geodesic
A $T(P)$-Theorem for Zygmund Spaces on Domains
Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 38-56

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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. 
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     author = {A. V. Vasin and E. Doubtsov},
     title = {A $T(P)${-Theorem} for {Zygmund} {Spaces} on {Domains}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {38--56},
     publisher = {mathdoc},
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     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a2/}
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A. V. Vasin; E. Doubtsov. A $T(P)$-Theorem for Zygmund Spaces on Domains. Matematičeskie zametki, Tome 114 (2023) no. 1, pp. 38-56. http://geodesic.mathdoc.fr/item/MZM_2023_114_1_a2/