Convergence of logarithmic means of quadratical partial sums of double Fourier series

TL;DR

This paper studies the convergence and divergence behavior of logarithmic means of quadratical partial sums in double Fourier series, focusing on functions within measure and Lebesgue spaces.

Contribution

It provides new insights into the convergence properties of logarithmic means of double Fourier series for functions in measure and Lebesgue spaces.

Findings

Identifies conditions for convergence of logarithmic means.

Establishes divergence scenarios for certain functions.

Analyzes behavior in measure and Lebesgue norms.

Abstract

In this paper we investigate some convergence and divergence properties of the logarithmic means of quadratical partial sums of double Fourier series of functions in the measure and in the $L$ Lebesgue norm.