Properties of certain moduli of continuity of integrable functions in $$$L_p$$$ spaces

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


The Potapov’s characteristic of functions of class $$$H^{\omega}_p$$$ is estimated from above in $$$L_p$$$ space.


function; continuity module; normed space; norm; splitting; Potapov's characteristic


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

Kolmogorov A.N., Fomin S.V. Elements of function theory and functional analysis, Moscow, 1972. (in Russian)




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