Order of magnitude of multiple Fourier coefficients of functions of bounded p-variation

摘要

For a Lebesgue integrable complex-valued function f defined over the n-dimensional torus denote the Fourier coefficient of f, where k = (k_1,...,k_n) ∈ ?~n. In this paper, defining the notion of bounded p-variation (p ≧ 1) for a function from [0, 2π]~n to ? in two diffierent ways, the order of magnitude of Fourier coefficients of such functions is studied. As far as the order of magnitude is concerned, our results with p = 1 give the results of Móricz [5] and Fül?p and Móricz [3].