Functions of bounded generalized second variation

T. I. Akhobadze

Sbornik. Mathematics, Tome 37 (1980) no. 2, pp. 261-294

Résumé

This paper introduces the classes $H_{\overline\Phi(n)}^{(2)}$ and $H_\Phi^{(2)}(n)$ of functions of $n$ variables. These classes, for $n=1$, are more general than the class of functions of bounded second variation introduced by F. I. Harsiladze, and in the case $n\geqslant2$ they contain the classes of functions of bounded generalized variation introduced by B. I. Golubov. Certain properties of functions of these classes are studied. A theorem on convergence and summability of Fourier series of functions from these classes is proved, and it is shown to be optimal in a certain sense. Bibliography: 27 titles.

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