This article is cited in 2 papers

Diameters of classes of continuous functions in the $L_p$ space

N. P. Korneichuk

Dnepropetrovsk State University

Abstract: In the $L_p(a,b)$ space the exact values of $n$-diameters $(n=1,2,\dots)$ are found of the class $H_\omega[a,b]$ of the functions $f(x)$ such that $|f(x')-f(x'')|\leqslant\omega(|x'-x''|)$, where $\omega(t)$ is a given continuity module which is convex upwards.

UDC: 517.5

Received: 28.12.1970

 English version: Mathematical Notes, 1971, 10:5, 719–723

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