L^1-convergence of complex double Fourier series

Kulwinder Kaur; S S Bhatia; Babu Ram

paper

L^1-convergence of complex double Fourier series

arXiv:math/0406074

Abstract

It is proved that the complex double Fourier series of an integrable function $f (x, y)$ with coefficients ${c_{j k}}$ 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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