Year: 2025
Type: article
Abstract: The Ahlfors-Beurling transform is one of the important operators in complex analysis. It is the "Hilbert transform" on complex plane. This transform plays an essential role in applications to the theory of quasiconformal mappings and to the Beltrami equation with discontinuous coeffcients. Therefore, approximations of the Ahlfors-Beurling transform are of great interest. This article is devoted to the approximation of the Ahlfors- Beurling transform in the Lebesgue spaces. We prove that the approximating operators are bounded maps in the Lebesgue spaces and converges strongly to the Ahlfors-Beurling transform
Source: Baku Mathematical Journal
Authors: Rashid A. Aliev, Lale Sh. Alizade
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4414759399
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