Geodesic
On deformation of certain functional classes in the~spaces $C(T^m)$ and~$L(T^m)$
Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1209-1224

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The problem of violation of the invariance of the functional classes $H(\omega_1,\dots,\omega_m;C(T^m))$ and $H(\omega_1,\dots,\omega_m;L(T^m))$ $(m\geqslant 2)$ under a multidimensional conjugation operator $\widetilde f_B$ is studied in the case when the moduli of continuity $\omega_i$ $(i=1,\dots,m)$ satisfy Zygmund's condition. Direct estimates are obtained and sharpness of these estimates is established. 
@article{SM_2001_192_8_a5,
     author = {M. M. Lekishvili and A. N. Danelia},
     title = {On deformation of certain functional classes in the~spaces $C(T^m)$ and~$L(T^m)$},
     journal = {Sbornik. Mathematics},
     pages = {1209--1224},
     publisher = {mathdoc},
     volume = {192},
     number = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_8_a5/}
}
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M. M. Lekishvili; A. N. Danelia. On deformation of certain functional classes in the~spaces $C(T^m)$ and~$L(T^m)$. Sbornik. Mathematics, Tome 192 (2001) no. 8, pp. 1209-1224. http://geodesic.mathdoc.fr/item/SM_2001_192_8_a5/