Multiple trigonometric series with lexicographically monotone coefficients
The author considers series of the type described in the title on the n- dimensional torus. He imposes an additional hypothesis on the growth of the coefficients, which he shows is always satisfied for a trigonometric series that is the Fourier series of an \(L_ p\)-function, \(1<p<\infty.\) Under these conditions he shows that the series is Pringsheim-convergent almost everywhere for \(p>n,\) but with \(p=n\) there exists an \(L_ p\)- function whose Fourier series has lexicographically monotone coefficients and diverges almost everywhere when arranged cubically.
scientific article; zbMATH DE number 4180038