Absolute Convergence of the Double Fourier-Franklin Series

Сибирский математический журнал

article

G. G. Gevorkyan¹  M. G. Grigoryan¹ 

[1] Yerevan State University

关键词: double Fourier series;    Franklin system;    absolute convergence;   

DOI  :  10.1134/S0037446620030039

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We prove that, for every 0 1 − ϵ such that, for all f ∈ L1(T) and 0 < η < 1, we can find $$\tilde f \in {L^1}(T)$$ with $$\int\!\!\!\int_T {{\rm{|}}f(x,y) - \tilde f(x,y){\rm{|}}dxdy \le \eta } $$ coinciding with f(x, y) on E whose double Fourier-Franklin series converges absolutely to f almost everywhere on T.

【 授权许可】

CC BY