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Mat. Zametki, 1978, Volume 23, Issue 3, Pages 361–372 (Mi mz8151)  

This article is cited in 5 scientific papers (total in 5 papers)

Conjugate functions of several variables in the class $\operatorname{Lip}_\alpha$

M. M. Lekishvili

Tbilisi State University

Abstract: It is known that if a function $f$ of a single variable belongs to the class $\operatorname{Lip}(\alpha,C(\mathbf T))$ $(0<\alpha<1)$, then its conjugate function also belongs to the same class; in other words, the class $\operatorname{Lip}(\alpha,C(\mathbf T))$ $(0<\alpha<1)$ is invariant with respect to the operator of conjugation acting in it. In the two-dimensional case the class $\operatorname{Lip}(\alpha,C(\mathbf T^2))$ $(0<\alpha<1)$ is no longer invariant with respect to conjugate functions of two variables. Here a final result elucidating the full character of violation of invariance of the class $\operatorname{Lip}(\alpha,C(\mathbf T^N))$ $(0<\alpha<1)$ with respect to the multidimensional conjugation operator acting in it is established.

Full text: PDF file (786 kB)

English version:
Mathematical Notes, 1978, 23:3, 196–203

Bibliographic databases:

UDC: 517.5
Received: 24.06.1976

Citation: M. M. Lekishvili, “Conjugate functions of several variables in the class $\operatorname{Lip}_\alpha$”, Mat. Zametki, 23:3 (1978), 361–372; Math. Notes, 23:3 (1978), 196–203

Citation in format AMSBIB
\Bibitem{Lek78}
\by M.~M.~Lekishvili
\paper Conjugate functions of several variables in the class $\operatorname{Lip}_\alpha$
\jour Mat. Zametki
\yr 1978
\vol 23
\issue 3
\pages 361--372
\mathnet{http://mi.mathnet.ru/mz8151}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=481923}
\zmath{https://zbmath.org/?q=an:0467.42013|0418.42009}
\transl
\jour Math. Notes
\yr 1978
\vol 23
\issue 3
\pages 196--203
\crossref{https://doi.org/10.1007/BF01651431}


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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. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Okulov, “Multidimensional analogue of a theorem of Privalov”, Sb. Math., 186:2 (1995), 257–269  mathnet  crossref  mathscinet  zmath  isi
    3. V. A. Okulov, “A multidimensional analog of a theorem due to Zygmund”, Math. Notes, 61:5 (1997), 600–608  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. M. M. Lekishvili, A. N. Danelia, “Multidimensional conjugation operators and deformations of the classes $Z(\omega^{(2)};C(T^m))$”, Math. Notes, 63:6 (1998), 752–759  mathnet  crossref  crossref  mathscinet  zmath  isi
    5. M. M. Lekishvili, A. N. Danelia, “On deformation of certain functional classes in the spaces $C(T^m)$ and $L(T^m)$”, Sb. Math., 192:8 (2001), 1209–1224  mathnet  crossref  crossref  mathscinet  zmath  isi
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