Abstract In this paper, we investigate the absolute convergence of Fourier series of functions in several variables for an odd-dimensional space when these functions have continuous partial derivatives. It should be noted that similar properties for an even-dimensional space were given in [L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 2015, 9, 12–21; translation in Russian Math. (Iz. VUZ) 59 (2015), no. 9, 9–17]. The obtained results are the best possible in a certain sense.

中文翻译：

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奇维空间的一些性质

摘要 在本文中，我们研究了当这些函数具有连续偏导数时，奇维空间中几个变量的傅立叶级数函数的绝对收敛性。应该注意的是，偶数维空间的类似性质在 [LD Gogoladze 和 VS Tsagareishvili，关于多个傅立叶级数的绝对收敛（俄文），Izv 中给出。维斯。乌切本。扎维。垫。2015, 9, 12–21; 俄语数学翻译。(Iz. VUZ) 59 (2015)，没有。9, 9–17]。得到的结果在某种意义上是最好的。