Inheritance of smoothness by extremal functions in Bergman spaces \(A_p\) for \(0<p<\infty \). (English. Russian original) Zbl 1476.30169

Burchaev, Kh. Kh.; Ryabykh, G. Yu.

Math. Notes 110, No. 2, 167-185 (2021); translation from Mat. Zametki 110, No. 2, 170-191 (2021).

Summary: 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.

MSC:

30H20

Bergman spaces and Fock spaces

Keywords:

Bergman space; extremal functions for linear functionals

References:

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