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. 
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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/

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