Abstract
We study the multipliers of multiple Fourier series
for a regular system on anisotropic Lorentz spaces.
In particular, the sufficient conditions for a sequence of
complex numbers {λk}k∈Zn in order to make it a multiplier
of multiple trigonometric Fourier series from Lp[0; 1]n to
Lq[0; 1]n , p > q. These conditions include conditions Lizorkin
theorem on multipliers.
A new note on factored infinite series and trigonometric Fourier series
