This article is cited in 3 papers

A multidimensional analog of a theorem due to Zygmund

V. A. Okulov

M. V. Lomonosov Moscow State University

Abstract: Zygmund proved an inequality describing the dependence of the modulus of continuity of the adjoint function on that of the original function lying in the space of $2\pi$-periodic continuous functions. The present article contains estimates of partial moduli of continuity of the adjoint function of several variables in the space $C$. Examples show that these estimates are sharp.

UDC: 517.518.475

Received: 27.11.1995

DOI: 10.4213/mzm1553

 English version: Mathematical Notes, 1997, 61:5, 600–608

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