L1-convergence of complex double Fourier series
Abstract
It is proved that the complex double Fourier series of an integrable function f(x,y) with coefficients \cjk\ 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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