𝐿1-Convergence of Complex Double Fourier Series

[摘要] It is proved that the complex double Fourier series of an integrable function 𝑓(𝑥, 𝑦) with coefficients {𝑐𝑗𝑘} satisfying certain conditions, will converge in 𝐿1-norm. The conditions used here are the combinations of Tauberian condition of Hardy–Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.

[学科分类] 数学（综合）

[关键词] Complex double Fourier series;𝐿1-convergence of Fourier series;Cesàromeans;de Ia Vallée-Poussin means;Tauberian condition of Hardy–Karamata kind.