Abstract In this paper, we investigate the Fourier partial sums with respect to a general orthonormal system (ONS) for functions belonging to the class C L C₋, that is, functions whose derivatives belong to the Lipschitz class Lip 1 Lip1. It is well known that the fact a function f (nonzero) belongs to a differential class does not guarantee the boundedness of its Fourier sums with respect to a general ONS. We establish certain conditions to be satisfied by the functions in the orthonormal system such that the Fourier partial sums of any function with derivatives from the Lipschitz class are bounded a. e. on 0, 1 0, 1. The obtained results are optimal in a certain sense.
Tutberidze et al. (Sat,) studied this question.