This article is cited in 2 papers

The integrability of conjugate functions

O. D. Tsereteli

A. M. Razmadze Mathematics Institute, Academy of Sciences of the Georgian SSR

Abstract: For any function $f$ of $L(0,2\pi)$, we prove that there is a function $\varphi\in L(0,2\pi)$ such that $|\varphi(x)|=|f(x)|$ almost everywhere and $\tilde{\varphi}\in L(0,2\pi)$, where $\tilde{\varphi}$ is the conjugate of $\varphi$.

UDC: 517.5

Received: 01.04.1968

 English version: Mathematical Notes, 1968, 4:4, 768–770

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