Geodesic
Local smoothness of the conjugate functions
Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 31-59

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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     author = {M. I. Dyachenko},
     title = {Local smoothness of the conjugate functions},
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M. I. Dyachenko. Local smoothness of the conjugate functions. Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 31-59. http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a1/