Geodesic
Multidimensional conjugation operators and deformations of the classes $Z(\omega^{(2)};C(T^m))$
Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 853-861

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The smoothness of conjugate functions of several variables is studied in terms of the second moduli of smoothness. It is proved that in a sufficiently general case the invariance of the classes considered is violated in just the same way as for classes specified by moduli of continuity. 
@article{MZM_1998_63_6_a5,
     author = {M. M. Lekishvili and A. N. Danelia},
     title = {Multidimensional conjugation operators and deformations of the classes $Z(\omega^{(2)};C(T^m))$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {853--861},
     publisher = {mathdoc},
     volume = {63},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a5/}
}
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M. M. Lekishvili; A. N. Danelia. Multidimensional conjugation operators and deformations of the classes $Z(\omega^{(2)};C(T^m))$. Matematičeskie zametki, Tome 63 (1998) no. 6, pp. 853-861. http://geodesic.mathdoc.fr/item/MZM_1998_63_6_a5/