L^1-convergence of complex double Fourier series

Details L^1-convergence of complex double Fourier series L^1-convergence of complex double Fourier series

2004-06-04

arxiv.org/abs/math/0406074v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 4, November 2003, pp. 355-363

Mathematics

Functional Analysis

9 pages, no figures, no tables

Scientific paper

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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