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 $H(\omega_1,\dots,\omega_m;C(T^m))$ 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.

UDC: 517.51

MSC: Primary 42A50; Secondary 42B05, 42B20

Received: 21.08.2000

DOI: 10.4213/sm589

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

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