On the convergence of multiple Fourier series of functions of bounded partial generalized variation

TL;DR

This paper investigates the conditions under which multiple Fourier series of functions with bounded partial generalized variation converge, establishing necessary and sufficient criteria based on the sequence defining the variation.

Contribution

It provides new necessary and sufficient conditions on the sequence b1 for the convergence of multiple Fourier series of functions with bounded partial b1-variation.

Findings

Identifies conditions on b1 for convergence

Establishes equivalence of necessary and sufficient conditions

Advances understanding of Fourier series convergence for generalized variation functions

Abstract

The convergence of multiple Fourier series of functions of bounded partial $% \Lambda$-variation is investigated. The sufficient and necessary conditions on the sequence $\Lambda=\{\lambda_n\}$ are found for the convergence of multiple Fourier series of functions of bounded partial $\Lambda$-variation.