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. 
@article{EMJ_2011_2_2_a1,
     author = {M. I. Dyachenko},
     title = {Local smoothness of the conjugate functions},
     journal = {Eurasian mathematical journal},
     pages = {31--59},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a1/}
}
TY  - JOUR
AU  - M. I. Dyachenko
TI  - Local smoothness of the conjugate functions
JO  - Eurasian mathematical journal
PY  - 2011
SP  - 31
EP  - 59
VL  - 2
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a1/
LA  - en
ID  - EMJ_2011_2_2_a1
ER  - 
%0 Journal Article
%A M. I. Dyachenko
%T Local smoothness of the conjugate functions
%J Eurasian mathematical journal
%D 2011
%P 31-59
%V 2
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a1/
%G en
%F EMJ_2011_2_2_a1
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/

[1] N. K. Bari, Trigonometrical series, Fizmatgiz, Moscow, 1961 (in Russian)

[2] N. K. Bari, S. B. Stechkin, “Best approximation and differential properties of two approximate functions”, Trudy Moscow Mathematical Society, 5, 1956, 483–522 (in Russian) | MR | Zbl

[3] Izvestiya Mathematics, 73:4 (2009), 655–668 | DOI | MR | Zbl

[4] Proceedings of the Steklov Institute of Mathematics, 269, 2010, 46–56 | DOI | MR | Zbl

[5] M. I. Dyachenko, Local properties of functions and Fourier series decompositions, Candidate's degree thesis, Moscow State University, Moscow, 1980 (in Russian)

[6] M. I. Dyachenko, About local properties of the conjugate functions, Deposited in VINITI, January 6, 1981 (in Russian)

[7] Russian Mathematics (Izvestiya VUZ. Matematika), 26:1 (1982), 10–19 | MR | MR | Zbl

[8] G. Freud, “An approximation theoretically study of the structure of real functions”, Stud. Sci. Math. Hung., 5:1–2 (1970), 141–150 | MR | Zbl

[9] N. N. Luzin, Integral and trigonometrical series, Gostehizdat, Moscow, 1951 (in Russian) | MR

[10] Proceedings of the Steklov Institute of Mathematics, 255, 2006, 185–202 | DOI | MR

[11] E. Nursultanov, S. Tikhonov, N. Tleukhanova, “Norm inequalities for convolution operators”, Comptes Rendus Acad. Sci. Paris, Ser. 1, 347 (2009), 1385–1388 | DOI | MR | Zbl

[12] I. I. Privaloff, “Sur les fonctions conjuguees”, BSMF, 44 (1916), 100–103 | MR

[13] M. Riesz, “Sur les fonctions conjuguees”, Math. Zeit., 27 (1927), 218–244 | DOI | MR | Zbl

[14] M. Salay, “Uber eine locale variante des Priwalovshen Satzes”, Stud. Sci. Math. Hung., 6:3–4 (1971), 427–429 | MR

[15] P. L. Ul'yanov, “On some equivalence conditions of convergence of series and integrals”, Uspekhi matematicheskikh nauk, 8:6 (1953), 133–141 (in Russian) | MR | Zbl

[16] P. L. Ul'yanov, “On modules of continuity and Fourier coefficients”, Vestnik Moscow State University, Ser. I, 1961, no. 1, 37–52 (in Russian) | MR