On the generalized \(\beta\)-absolute convergence of single and multiple Fourier series (Q6542691)

In this article, the author provides sufficient conditions for the generalized absolute convergence of multiple Fourier series of a function of \(p\)-\((\Lambda^{1},\dots,\Lambda^{N})\)-bounded variation. Various authors already proved such results for the single Fourier series and multiple Fourier series. The present results generalize the earlier results in such a way that the author takes a nondecreasing sequence \(\Lambda=\{\lambda_{k}\}^{1}_{\infty}\) of positive numbers such that \(\sum_{k}\frac{1}{\lambda_{k}}\) diverges. The absolute convergence is first proved for single Fourier series and then extended to double and multiple Fourier series.