L¹-convergence of complex double Fourier series

2004/06/04 by Kulwinder Kaur, S S Bhatia, Babu Ram
Mathematics · #math.FA #msc:42A20 #msc:42A32

paper · pdf

published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 113, No. 4, November 2003, pp. 355-363 · 9 pages, no figures, no tables

arxiv created 2004/06/04 · arxiv updated 2009/12/01

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 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.

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