On classification of integrable functions

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

Abstract


The questions of the classification of the integrable on the segment functions were considered in this article. Estimates for modulus of continuity are obtained.

Keywords


modulus of continuity; integral; weight function

References


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Potapov M.K. "On theorems of Jackson type in $$$L_p$$$ metric", Dokl. AN SSSR, 1956; 111(6): pp. 1185-1188. (in Russian)

Timan A.F. Approximation theory for real-variable functions, Fizmatgiz, Moscow, 1960; 624 p. (in Russian)

Ditzian Z., Totik V. Moduli of smoothness, Springer-Verlag, Berlin, 1993; 225 p. doi:10.1007/978-1-4612-4778-4

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

Sedunova V.V. "Properties of certain moduli of continuity of integrable functions in $$$L_p$$$ spaces", Res. Math., 2014; 22(19): pp. 80-91. (in Ukrainian) doi:10.15421/241410

Motornyi V.P. "On the classes of M.K. Potapov", Res. Math., 2014; 22(19): pp. 62-72. (in Russian) doi:10.15421/241408




DOI: https://doi.org/10.15421/241506

  

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Copyright (c) 2015 V.P. Motornyi, V.V. Sedunova

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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