BMO-estimation and Almost Everywhere Exponential Summability of Quadratic Partial Sums of Double Fourier Series

TL;DR

This paper establishes BMO-estimates for quadratic partial sums of double Fourier series, leading to almost everywhere exponential summability results, advancing understanding of convergence properties in Fourier analysis.

Contribution

It introduces a novel BMO-estimation technique for quadratic partial sums, enabling new almost everywhere exponential summability results for double Fourier series.

Findings

BMO-estimation for quadratic partial sums proved

Almost everywhere exponential summability established

Enhanced convergence understanding in Fourier series

Abstract

It is proved a $BMO$-estimation for quadratic partial sums of two-dimensional Fourier series from which it is derived an almost everywhere exponential summability of quadratic partial sums of double Fourier series.