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Mat. Sb., 2001, Volume 192, Number 8, Pages 123–138 (Mi msb589)  

On deformation of certain functional classes in the spaces $C(T^m)$ and $L(T^m)$

M. M. Lekishvili, A. N. Danelia

Tbilisi Ivane Javakhishvili State University

Abstract: The problem of violation of the invariance of the functional classes $H(\omega_1,…,\omega_m;C(T^m))$ and $H(\omega_1,…,\omega_m;L(T^m))$ $(m\geqslant 2)$ under a multidimensional conjugation operator $\widetilde f_B$ is studied in the case when the moduli of continuity $\omega_i$ $(i=1,…,m)$ satisfy Zygmund's condition. Direct estimates are obtained and sharpness of these estimates is established.

DOI: https://doi.org/10.4213/sm589

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English version:
Sbornik: Mathematics, 2001, 192:8, 1209–1224

Bibliographic databases:

UDC: 517.51
MSC: Primary 42A50; Secondary 42B05, 42B20
Received: 21.08.2000

Citation: M. M. Lekishvili, A. N. Danelia, “On deformation of certain functional classes in the spaces $C(T^m)$ and $L(T^m)$”, Mat. Sb., 192:8 (2001), 123–138; Sb. Math., 192:8 (2001), 1209–1224

Citation in format AMSBIB
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