Inheritance of Smoothness by Extremal Functions in Bergman Spaces $A_p$ for $0<p<\infty$

Kh. Kh. Burchaev^a, G. Yu. Ryabykh<sup>b

a</sup> Chechen State University, Grozny
^b Don State Technical University, Rostov-on-Don

Abstract: We study the problem of how extremal functions for linear functionals over a Bergman space are influenced by the properties of the functions generating these functionals. For different classes of generating functions, we obtain a sufficiently exact description of qualitative properties of the corresponding extremal functions. The method developed here can be used to study similar problems in Hardy spaces.

Keywords: Bergman space, linear functional, extremal function, existence, Lipschitz class, derivative, orthogonality, property of being Hilbert.

UDC: 517.53/57

Received: 09.06.2019
Revised: 29.03.2021

DOI: 10.4213/mzm12470

 English version: Mathematical Notes, 2021, 110:2, 167–185

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