On the convergence of Ces\`{a}ro means of negative order of double trigonometric Fourier series of functions of bounded partial generalized variation

TL;DR

This paper investigates the convergence conditions of Cesàro means of negative order for double trigonometric Fourier series of functions with bounded partial mbda-variation, establishing necessary and sufficient criteria based on the sequence mbda.

Contribution

It provides the first comprehensive characterization of convergence conditions for Cesàro means of negative order in this context, linking sequence properties to convergence behavior.

Findings

Identifies necessary and sufficient conditions on mbda for convergence.

Establishes convergence criteria for functions of bounded partial mbda-variation.

Extends understanding of Fourier series convergence with Cesàro means of negative order.

Abstract

The convergence of Ces\`{a}ro means of negative order of double trigonometric Fourier series of functions of bounded partial $\Lambda$-variation is investigated. The sufficient and neccessary conditions on the sequence $\Lambda =\{\lambda_{n}\}$ are found for the convergence of Ces\`{a}ro means of Fourier series of functions of bounded partial $\Lambda$-variation.