Extension of a Theorem of Ferenc Lukács from Single to Double Conjugate Series

A theorem of Ferenc Lukács states that if a periodic function f is integrable in the Lebesgue sense and has a discontinuity of the first kind at some point x, then the mth partial sum of the conjugate series of its Fourier series diverges at x at the rate of logm. The aim of the present paper is to...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 259; no. 2; pp. 582 - 595
Main Author:	MORICZ, Ferenc
Format:	Journal Article
Language:	English
Published:	San Diego, CA Elsevier Inc 15.07.2001 Elsevier
Subjects:	conjugate series criterion of nonatomic measure Exact sciences and technology Fourier analysis Fourier series function of bounded variation over a rectangle in the sense of Hardy and Krause induced Borel measure Mathematical analysis Mathematics rate of divergence rectangular partial sum Sciences and techniques of general use sector limits of a function in two variables rectangular partial sum rate of divergence function of bounded variation over a rectangle in the sense of Hardy and Krause induced Borel measure sector limits of a function in two variables Fourier series conjugate series criterion of nonatomic measure Mathematical series Rate of divergence Conjugate series Partial sum Functional analysis Borel measure Ferenc Lukacs theorem
ISSN:	0022-247X, 1096-0813
Online Access:	Get full text
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