Restricted Beurling transforms on Campanato spaces

2016/04/26 by Evgueni Doubtsov, Doubtsov, Evgueni, Andrei V. Vasin +1
Mathematics · #30C62 #30H30 #42B20 #46E15 #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1604.07670

openalex publication_date 2016/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℂ be a bounded domain with C^1,ω-smooth boundary, where ω is a Dini-smooth modulus of continuity. We prove that the restricted Beurling transform is bounded on the Campanato space BMO_ω(Ω).

Citations

• Generalizations of Lipschitz spaces and an application to Hardy spaces and bounded mean oscillation

Related

• Regularity of C¹ and Lipschitz domains in terms of the Beurling transform
• Smoothness of the Beurling transform in Lipschitz domains
• T1 theorem for Campanato spaces on domains
• Causal sparse domination of Beurling maximal regularity operators
• Boundedness of variation, oscillation and maximal differential transform on BMO space