This article is cited in 3 papers

A generalization of a theorem of M. Riesz to the case of functions of several variables

L. V. Zhizhiashvili

Tiflis State University

Abstract: The following theorem was proved by M. Riesz: If $f(x)\in L(-\pi,\pi)$, $f(x)\geqslant0$ and the conjugate function $f(x)$ is also integrable on $[-\pi,\pi]$, then $f(x)\in L\log^+L$. The analog of this theorem for functions of several variables is established.

UDC: 517.5

Received: 05.01.1968

 English version: Mathematical Notes, 1968, 4:3, 655–661

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