This article is cited in 4 papers

Functions of bounded $p$-variation with given order of modulus of $p$-continuity

A. P. Terekhin

Saratov State University

Abstract: We construct continuous functions for which the modulus of $p$-continuity tends to zero with given order in Wiener's sense
$$ V^p(\delta;f)=\sup\sum_i|f(x_i)-f(x_{i-1})|^p\qquad(p>1) $$
(the upper bound is taken over partitions satisfying the condition $x_i-x_{i-1}\leqslant\delta$).

UDC: 517.5

Received: 30.06.1971

 English version: Mathematical Notes, 1972, 12:5, 751–755

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