Page
153-162
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
Recommended Citation
Baku State University, Baku, Azerbaijan; Aliev, Rashid A.; and Alizade, Lale Sh.
(2025)
"Approxımatıon of the Ahlfors-Beurlıng transform in the Lebesgue spaces,"
Baku Mathematical Journal: Vol. 4:
Iss.
2, Article 2.
DOI: 10.32010/j.bmj.2025.11
Available at:
https://www.bakumathj.org/home/vol4/iss2/2