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