George Tkebuchava

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

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.

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

MSC 2000: 42C15, 41A63, 41A58