This article is cited in 4 papers

On the moduli of continuity of equimeasurable functions in the classes $\varphi(L)$

P. Oswald

Odessa State University, USSR

Abstract: In the note we establish a number of relations between the moduli of continuity of the equimeasurable functions $f(x)$ and $f^*(x)$. In particular, for $f(x)\in L_p(0,1)$, $1\le p<\infty$, we have proved the inequality $\omega_p(\delta,f)\ge\frac12\omega_p(\delta,f^*),\quad\delta\in\Bigl[0,\frac12\Bigr]$.

UDC: 517

Received: 19.06.1973

 English version: Mathematical Notes, 1975, 17:2, 134–141

Bibliographic databases:

• 
•