Discrete Ahlfors-Beurling transform and its properties. (English) Zbl 1468.44003

Aliev, Rashid A.; Ahmadova, Aynur N.

Probl. Anal. Issues Anal. 9(27), No. 2, 3-15 (2020).

Summary: 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.

MSC:

44A15	Special integral transforms (Legendre, Hilbert, etc.)
39A12	Discrete version of topics in analysis
46B45	Banach sequence spaces
42B35	Function spaces arising in harmonic analysis

Keywords:

discrete Ahlfors-Beurling transform; Lebesgue spaces; boundedness

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