On the Partial Sums of the Fourier Series of Functions of Bounded Variation

S. Banach [Sur la divergence des séries orthogonales. Studia Math., 1940, vol. 9, pp. 139–155] proved that for any function $f(x)\in L_2(I)$ $(I=[0,1]$, $f(x)\not\sim 0)$ there exists an orthonormal system (ONS) $(\varphi_n(x))$ such that $\varlimsup\limits_{n\to \infty} |S_n(f,x)|=+\infty$ almost everywhere on $I$, where $S_n(f,x)$ are the partial sums of the Fourier series of a function $f(x)$ with respect to the system $(\varphi_n(x))=\Phi$.
This paper finds necessary and sufficient conditions which should be satisfied by ONS so that the partial sums of the Fourier series of functions with finite variation be uniformly bounded on $I$.