Calder'on-Zygmund operators on Zygmund spaces on domains.

2017/12/30 by Andrei V. Vasin, Vasin, Andrei V.
Computer Science · Mathematics · #42B20 #46E25 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1801.01023

openalex publication_date 2017/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a bounded Lipschitz domain D\⊂ \ℝ^d and a\nCalder 'on-Zygmund operator T, we study the relations between smoothness\nproperties of \∂ D and the boundedness of T on the Zydmund space\n\C_\ω(D) defined for a general growth function \ω. In\nthe proof we obtain a T(P) theorem for the Zygmund spaces, when one checks\nboundedness not only of the characteristic function, but a finite collection of\npolynomials restricted to the domain. Also, a new form of extra cancellation\nproperty of the even Calder 'on-Zygmund operators in polynomial domains is\nstated.\n

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