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 Eurasian Math. J., 2011, Volume 2, Number 2, Pages 31–59 (Mi emj51)

Local smoothness of the conjugate functions

M. I. Dyachenko

Department of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: In the paper the author deals with the following problem: what can we say about the behaviour of the conjugate function at a fixed point, if the global smoothness as well as the behaviour at this point of the original function are known? Sharp results on this and related problems are obtained.

Keywords and phrases: conjugate functions, local smoothness.

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MSC: 42A50
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Citation: M. I. Dyachenko, “Local smoothness of the conjugate functions”, Eurasian Math. J., 2:2 (2011), 31–59

Citation in format AMSBIB
\Bibitem{Dya11} \by M.~I.~Dyachenko \paper Local smoothness of the conjugate functions \jour Eurasian Math. J. \yr 2011 \vol 2 \issue 2 \pages 31--59 \mathnet{http://mi.mathnet.ru/emj51} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2910830} \zmath{https://zbmath.org/?q=an:1271.42009} 

• http://mi.mathnet.ru/eng/emj51
• http://mi.mathnet.ru/eng/emj/v2/i2/p31

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This publication is cited in the following articles:
1. M. I. Dyachenko, E. D. Nursultanov, S. Yu. Tikhonov, “Global and local smoothness of the Hilbert transforms”, Proc. Steklov Inst. Math., 280 (2013), 169–180
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