L¹-convergence of complex double Fourier series
classification
🧮 math.FA
keywords
complexdoublefourierseriesconditionsbraycasecertain
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It is proved that the complex double Fourier series of an integrable function $f(x,y)$ with coefficients $\{c_{jk}\}$ satisfying certain conditions, will converge in $L^{1}$-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.
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