Uniform Convergence of Double Fourier-Legendre series of Functions of Bounded Generalized Variation

TL;DR

This paper investigates the conditions under which double Fourier-Legendre series uniformly converge for functions with bounded harmonic variation and bounded partial bc-variation, expanding understanding of convergence criteria.

Contribution

It provides new results on uniform convergence of double Fourier-Legendre series for functions with specific bounded variation properties.

Findings

Established uniform convergence for functions of bounded harmonic variation.

Extended convergence results to functions with bounded partial bc-variation.

Contributed to the theory of Fourier-Legendre series in function spaces.

Abstract

The Uniform convergence of double Fourier-Legendre series of function of bounded Harmonic variation and bounded partial $\Lambda $-variation are investigated.