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On deformation of certain functional classes in the spaces $$C(T^m)$$ and $$L(T^m)$$. (English. Russian original) Zbl 1035.42020
Sb. Math. 192, No. 8, 1209-1224 (2001); translation from Mat. Sb. 192, No. 8, 123-138 (2001).
In this paper the first author proves a nice theorem on the violation of the invariance of the functional class $$H(\omega_1,\dots, \omega_m; C(T^m))$$ – the second named author verifies the same with $$H(\omega_1,\dots, \omega_m; L(T^m))-(m\geq 2)$$ under a multidimensional conjugation operator $$\widetilde f_B$$ assuming that the moduli of continuities satisfy the Zygmund condition. Both prove the sharpness of the result.
##### MSC:
 42B35 Function spaces arising in harmonic analysis 42B25 Maximal functions, Littlewood-Paley theory 42B05 Fourier series and coefficients in several variables
##### Keywords:
functional class; Zygmund condition
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