On the coexistence of divergence and convergence phenomena for the Fourier-Haar series for non-negative functions

Michihiro Hirayama, Davit Karagulyan

Let $\{H_{n,m}{\}}_{n,m\in \mathbb{N}}$ be the two dimensional Haar system and $S_{n,m}f$ be the rectangular partial sums of its Fourier series with respect to some $f\in L^1([0,1)^2…