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Mat. Zametki, 1968, Volume 4, Issue 4, Pages 461–465 (Mi mz9468)  

This article is cited in 2 scientific papers (total 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 $\varphi$.

Full text: PDF file (430 kB)

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

Bibliographic databases:

UDC: 517.5
Received: 01.04.1968

Citation: O. D. Tsereteli, “The integrability of conjugate functions”, Mat. Zametki, 4:4 (1968), 461–465; Math. Notes, 4:4 (1968), 768–770

Citation in format AMSBIB
\Bibitem{Tse68}
\by O.~D.~Tsereteli
\paper The integrability of conjugate functions
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 4
\pages 461--465
\mathnet{http://mi.mathnet.ru/mz9468}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=236596}
\zmath{https://zbmath.org/?q=an:0175.35302}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 4
\pages 768--770
\crossref{https://doi.org/10.1007/BF01093717}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    2. Sh. V. Kheladze, “Convergence of Fourier series almost everywhere and in the $L$-metric”, Math. USSR-Sb., 35:4 (1979), 527–539  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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