A modulus of smoothness for some Banach function spaces

Ramazan Akgün

doi:10.3842/umzh.v75i8.970

Ramazan Akgün Department of Mathematics, Faculty of Arts and Sciences, Balikesir University, Turkey https://orcid.org/0000-0001-6247-8518

DOI: https://doi.org/10.3842/umzh.v75i8.970

Keywords: A constructive characterization

Abstract

UDC 517.5

Based on the Steklov operator, we consider a modulus of smoothness of functions in some Banach function spaces, which can be not translation invariant and establish its main properties. A constructive characterization of the Lipschitz class is obtained by using the Jackson-type direct theorem and inverse theorem of trigonometric approximation. As application, we present several examples of related (weighted) function spaces.

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