Geodesic
Inheritance of Smoothness by Extremal Functions in Bergman Spaces~$A_p$ for $0$
Matematičeskie zametki, Tome 110 (2021) no. 2, pp. 170-191

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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, Lipschitz class, derivative, orthogonality, property of being Hilbert.
Mots-clés : existence 
@article{MZM_2021_110_2_a1,
     author = {Kh. Kh. Burchaev and G. Yu. Ryabykh},
     title = {Inheritance of {Smoothness} by {Extremal} {Functions} in {Bergman} {Spaces~}$A_p$ for $0<p<\infty$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {170--191},
     publisher = {mathdoc},
     volume = {110},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_110_2_a1/}
}
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Kh. Kh. Burchaev; G. Yu. Ryabykh. Inheritance of Smoothness by Extremal Functions in Bergman Spaces~$A_p$ for $0