On classes of M.K. Potapov

V.P. Motornyi (Oles Honchar Dnipropetrovsk National University)


Estimates for modulus of continuity functions, that are integrable on the segment, are obtained.


modulus of continuity; integral; weight function


Potapov M.K. "On approximation of non-periodic functions by algebraic polynomials", Vestn. Mosk. un-ta, 1960; 4: pp. 14-25. (in Russian)

Potapov M.K. "On approximation by algebraic polynomials in $$$L_p$$$ metric", Researches on modern problems of constructive function theory, Moscow, 1961. (in Russian)

Motornyi V.P., Sedunova V.V. "Properties of certain moduli of continuity of integrable functions", Res. Math., 2013; 18: pp. 132-140. (in Ukrainian) doi:10.15421/241316

Motornyi V.P. "Approximation of functions by algebraic polynomials in $$$L_p$$$ metric", Izv. AN SSSR. Ser.: Matematika, 1971; 35(4): pp. 874-899. (in Russian) doi:10.1070/IM1971v005n04ABEH001122

Goncharov S.V. "On approximation of functions by algebraic polynomials in $$$L^p_{\rho}$$$ metric", Res. Math., 2009; 14: pp. 48-59. (in Russian)

DOI: https://doi.org/10.15421/241408



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