**George Tkebuchava**

## Integrability of the Majorant of the Fourier
Series Partial Sums with Respect to Bases

**Abstract:**

The majorant of Fourier series partial sums with respect to the system of
functions formed by the product of $L([0,1])$ space bases is considered. It is
proved that in any Orlicz space wider than $L(\log^{+}L)^{d}([0,1]^{d})$, $d\geq
1$, the set of functions with such a majorant is integrable on $[0,1]^{d}$ and
has the first Baire category.

**Keywords:**

Majorant of partial sums, Haar system, Orlicz space, bases in Banach spaces.

**MSC 2000:** 42C15, 41A63, 41A58