Geodesic
Singular integral operators on Zygmund spaces on
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 43-51 Cet article a éte moissonné depuis la source Math-Net.Ru

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Given a bounded Lipschitz domain $D\subset \mathbb{R}^d$ and a Calderón–Zygmund operator $T$, we study the relationship between smoothness properties of $\partial D$ and the boundedness of $T$ on the Zydmund space $\mathcal{C}_{\omega}(D)$ defined for a general growth function $\omega$. We prove a T(P)-theorem for the Zygmund spaces, checking the boundedness of $T$ on a finite collection of polynomials restricted to the domain. Also, we obtain a new form of an extra cancellation property for the even Calderón–Zygmund operators in polynomial domains. 
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     author = {A. V. Vasin},
     title = {Singular integral operators on {Zygmund} spaces on},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a2/}
}
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A. V. Vasin. Singular integral operators on Zygmund spaces on. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 43-51. http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a2/

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