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


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

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

Timan A.F. Theory of real-variable functions approximation, GIFML, Moscow, 1960; 624 p. (in Russian)

Ditzian Z., Totik V. Moduli of smoothness, Springer-Verlag, Berlin, 1993; 225 p.

Motornyi V.P., Sedunova V.V. "Properties of certain moduli of continuity of integrable functions", Dnipr. Univ. Math. Bull., 2013; 18: pp. 132-140. (in Ukrainian)

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)

Sedunova V.V. "Properties of certain moduli of continuity of integrable functions in $$$L_p$$$ spaces", Dnipr. Univ. Math. Bull., 2014; 22(19): pp. 80-91. (in Ukrainian)

Motornyi V.P. "On the classes of M.K. Potapov", Dnipr. Univ. Math. Bull., 2014; 22(19): pp. 62-72. (in Russian)




DOI: https://dx.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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