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

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
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### References:

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