On inequalities of Kolmogorov type for the functions being analytic in the disk

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241211

On inequalities of Kolmogorov type for the functions being analytic in the disk

S.B. Vakarchuk (Alfred Nobel Dnipropetrovsk University), https://orcid.org/0000-0002-2562-8844
M.B. Vakarchuk (Oles Honchar Dnipropetrovsk National University)

Abstract

Sharp inequality of Kolmogorov type is obtained in the Bergman space $$$B_2$$$ for functions being analytic in the unit disk. The application of this inequality to problems of the theory of approximation in the complex plane is presented too.

Keywords

Bergman space; intermediate derivative; inequality of Kolmogorov type; the best polynomial approximation

Full Text:

PDF (Русский)

References

Vakarchuk S.B., Shabozov M.Sh. "On widths of classes of functions, being analytic in the disk", Matem. sbornik, 2010; 201(8): pp. 3-22. (in Russian) doi:10.1070/SM2010v201n08ABEH004104

Vakarchuk S.B. "On inequalities of Kolmogorov type for certain Banach spaces of analytic functions", Some problems of analysis and differential topology: Sb. nauchn. tr., In-t matematiki AN Ukr.SSR, 1988; pp. 4-7. (in Russian)

Vakarchuk S.B., Vakarchuk M.B. "On multiplicative inequalities of Hardy-Littlewood-Polya type for analytic functions of one and two complex variables", Res. Math., 2010; 18(6/1): pp. 81-87. (in Russian)

Smirnov V.I., Lebedev N.A. Constructive theory of complex variable functions, Moscow-Leningrad, 1964; 438 p. (in Russian)