On the majorant of the partial sums of Fourier series with respect to bases (Q1337906)

In the investigation of the convergence of Fourier series with respect to various systems of functions, an important role is played by the majorant of the partial sums [see, for example, \textit{B. S. Kashin} and \textit{A. A. Saakyan}: ``Orthogonal series'' (1984; Zbl 0632.42017; English translation 1989; Zbl 0668.42011)]. In this paper we investigate the question of the integrability of such a majorant with respect to a system of functions formed by products of bases.