Absolute convergence of double trigonometric Fourier series and Walsh-Fourier Series

In the first part of our theses we give sufficient conditions for the absolute convergence of the double Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous fu...

Full description

Saved in:
Bibliographic Details
Main Author: Veres Antal
Other Authors: Móricz Ferenc
Format: Dissertation
Published: 2011-11-11
Subjects:
doi:10.14232/phd.690

mtmt:1919939
Online Access:http://doktori.ek.szte.hu/690
Description
Summary:In the first part of our theses we give sufficient conditions for the absolute convergence of the double Fourier series of f in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative in case f is an absolutely continuous function. Our results extend the classical theorems of Bernstein and Zygmund from single to double Fourier series. In the second part we give sufficient conditions for the absolute convergence of the double Walsh-Fourier series of a function. These sufficient conditions are formulated in terms of (either global or local) dyadic moduli of continuity and s-bounded fluctuation.