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L^1-convergence of complex double Fourier series

Kulwinder Kaur·S S Bhatia·Babu Ram
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Abstract

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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BibTeXRIS

Kulwinder Kaur, S S Bhatia, Babu Ram. 2004-06-04. L^1-convergence of complex double Fourier series. https://arxiv.org/abs/math/0406074

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