For a Lebesgue integrable complex-valued function f defined over the n-dimensional torus := [0, 2π) n , let (k) denote the Fourier coefficient of f, where k = (k 1, … k n ) ∈ ℤ n . In this paper, defining the notion of bounded p-variation (p ≧ 1) for a function from [0, 2π] n to ℜ 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 Fülöp and Móricz [3].
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机译：对于在n维环面上定义的Lebesgue可积复值函数f：= [0，2π） n ，令（k）表示f的傅立叶系数，其中k =（k 1 ，…k n ）∈ℤ n 。在本文中，以两种不同的方式定义从[0，2π] n 到function的函数的有界p变量（p≥1）的概念，该函数的傅立叶系数的量级功能的研究。就数量级而言，我们的p = 1的结果给出了Móricz[5]以及Fülöp和Móricz[3]的结果。
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