Rashid A. Aliev, Aynur N. Ahmadova, “Discrete Ahlfors–Beurling transform and its properties”, Probl. Anal. Issues Anal., 2020, Volume 9(27), Issue 2,Pages <nobr>3

Discrete Ahlfors–Beurling transform and its properties

Rashid A. Aliev^ab, Aynur N. Ahmadova^c

^a Baku State University, Baku, AZ 1148, Azerbaijan
^b Institute of Mathematics and Mechanics, NAS of Azerbaijan, Baku, AZ 1141, Azerbaijan
^c Sumgait State University, Sumgait, AZ 5008, Azerbaijan

Abstract: The Ahlfors–Beurling transform has been well studied on classical Lebesgue, Morrey, Sobolev, Besov, Campanato, etc. spaces. However, its discrete version is still not studied well. In this paper, we study the properties of the discrete Ahlfors–Beurling transform on discrete Lebesgue spaces.

Keywords: discrete Ahlfors–Beurling transform, Lebesgue spaces, boundedness.

UDC: 517.521.1, 517.518.13

MSC: 44A15, 40A05, 46B45, 42B35

Received: 06.12.2019
Revised: 05.04.2020
Accepted: 06.04.2020

Language: English

DOI: 10.15393/j3.art.2020.7390