AbstractIn this paper, we obtain sufficiency conditions for generalized β-absolute convergence ({0<\beta\leq 2}) of single and multiple Fourier series of functions of the class {\Lambda\text{-}\mathrm{BV}(p(n)\uparrow\infty,\varphi,[-\pi,\pi])} and the class {(\Lambda^{1},\Lambda^{2},\dots,\Lambda^{N})\text{-}\mathrm{BV}(p(n)\uparrow%
\infty,\varphi,[-\pi,\pi]^{N})}, respectively.
AbstractIn 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.
Criteria for absolute convergence of multiple fourier series
