@article {Moricz:May :0236-5294:323,
	author = "Moricz F. and Wade W.R.",
	title = "AN ANALOGUE OF A THEOREM OF FERENC LUKACS FOR DOUBLE WALSH-FOURIER SERIES",
	journal = "Acta Mathematica Hungarica",
	volume = "95",
	number = "4",
	year = "May ",
	abstract = "<P>A theorem of Ferenc Luk&aacute;cs states that if a periodic function f is integrable in Lebesgue&quot;s sense and has a discontinuity of first kind at some point \alpha, then the nth partial sum of the conjugate series to its trigonometric Fourier series at \alpha divided by \ln n converges to \pi^{-1} \big\{ f(\alpha - 0) - f(\alpha+ 0)\big\} as n\to \infty. An analogue of this theorem for Walsh&#150;Fourier series was proved by Rafat Riad. The main aim of the present paper is to extend the latter result from single to double Wals&#150;Fourier series. We consider also functions of two variables which are of bounded variation over a rectangle in the sense of Hardy and Krause. Among others, we present a proof of the existence of the so-called sector limits of such functions at each point.</P>",
	pages = "323-336",
	url = "http://www.ingentaconnect.com/content/klu/amhu/2002/00000095/00000004/00400437",
	keyword = "Walsh&#150;Paley system, Walsh series, conjugate Walsh series, rectangular partial sum, bounded variation over a rectangle in the sense of Hardy and Krause, discontinuity of first kind, sector limits of a function of two variables"
}