Order of magnitude of multiple Fourier coefficients of functions of bounded \(p\)-variation (Q625991)

The author defines the bounded \(p\)-variations for a function of several variables in such a way that for \(p=1\) these definitions reduce to the well known variations of Vitali and Hardy. The order of magnitude of the Fourier coefficients of a function of bounded \(p\)-variation depends on \(p\) and generalizes certain previous results, first of all those due to \textit{F. Móricz} [Analysis, München 22, No. ~4, 335--345 (2002; Zbl 1039.42009)] and to \textit{V. Fülöp and F. Móricz} [Acta Math. Hung. 104, No. ~1--2, 95--104 (2004; Zbl 1067.42006)].