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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
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