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Matematicheskie Zametki, 2021, Volume 110, Issue 2, Pages 170–191
DOI: https://doi.org/10.4213/mzm12470 (Mi mzm12470) 		 
Inheritance of Smoothness by Extremal Functions in Bergman Spaces $A_p$ for $0<p<\infty$

Kh. Kh. Burchaeva, G. Yu. Ryabykhb

a Chechen State University, Grozny
b Don State Technical University, Rostov-on-Don
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DOI: https://doi.org/10.4213/mzm12470
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.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00017
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00017.
Received: 09.06.2019
Revised: 29.03.2021
English version:
Mathematical Notes, 2021, Volume 110, Issue 2, Pages 167–185
DOI: https://doi.org/10.1134/S0001434621070191
Bibliographic databases:
Document Type: Article
UDC: 517.53/57
Language: Russian
Citation: Kh. Kh. Burchaev, G. Yu. Ryabykh, “Inheritance of Smoothness by Extremal Functions in Bergman Spaces $A_p$ for $0<p<\infty$”, Mat. Zametki, 110:2 (2021), 170–191; Math. Notes, 110:2 (2021), 167–185
Citation in format AMSBIB
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\pages 170--191
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