On inequalities of Kolmogorov type for the functions being analytic in the unit bicircle

S.B. Vakarchuk; M.B. Vakarchuk

doi:10.15421/241308

On inequalities of Kolmogorov type for the functions being analytic in the unit bicircle

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

Abstract

The sharp inequality of Kolmogorov type has been obtained in the space $$$\mathfrak{B}(U_2)$$$ for functions of two complex variables analytic in the unit bicircle.

Keywords

unit bicircle; intermediate derivative; inequality of the Kolmogorov type

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References

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)

Vakarchuk M.B., Vakarchuk S.B. "On inequalities of Kolmogorov type for analytic functions of one and many variables", Abstracts of Intern. Conf. "Approxim. Theory and Appl." in memory of N.P. Korneichuk, Dnipropetrovsk, 2010; p. 27. (in Russian)

Vakarchuk S.B., Vakarchuk M.B. "On inequalities of Kolmogorov type for the functions being analytic in the circle", Res. Math., 2012; 20(6/1): pp. 82-88. (in Russian) doi:10.15421/241211

Hardy G.H., Littlewood J.E., Polya G. Inequalities, IL, Moscow, 1948; 456 p. (in Russian)