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.
References
[1] G. Aleksič, Convergence Problems of Orthogonal Series (in Russian), Izdat. Inostran. Lit., Moscow, 1963. Search in Google Scholar
[2] L. Gogoladze and V. Tsagareishvili, On the divergence of Fourier series of functions in several variables, Anal. Math. 39 (2013), no. 3, 163–178. 10.1007/s10476-013-0301-1Search in Google Scholar
[3] L. Gogoladze and V. Tsagareishvili, Absolute convergence of multiple Fourier–Haar series, Georgian Math. J. 21 (2014), no. 1, 69–74. 10.1515/gmj-2013-0029Search in Google Scholar
[4] L. D. Gogoladze and V. S. Tsagareishvili, On absolute convergence of multiple Fourier series (in Russian), Izv. Vyssh. Uchebn. Zaved. Mat. (2015), no. 9, 12–21; translation in Russian Math. (Iz. VUZ) 59 (2015), no. 9, 9–17. 10.3103/S1066369X15090029Search in Google Scholar
[5] P. L. Ul’janov, On Haar series (in Russian), Mat. Sb. (N. S.) 63(105) (1964), 356–391. Search in Google Scholar
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