A modulus of smoothness for some Banach function spaces

Keywords: A constructive characterization


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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How to Cite
Akgün, R. “A Modulus of Smoothness for Some Banach Function Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 8, Aug. 2023, pp. 1015 -31, doi:10.3842/umzh.v75i8.970.
Research articles