In this paper, we generalized a known theorem dealing with absolute weighted
arithmetic mean summability of infinite series by using a quasi-f-power
increasing sequence instead of a quasi-?-power increasing sequence. And we
applied it to the trigonometric Fourier series
Abstract
In this paper, some known results on the absolute Riesz summability factors of infinite series and trigonometric Fourier series have been generalized for the
{\lvert\bar{N},p_{n};\theta_{n}\rvert_{k}}
summability method. Some new and known results are also obtained.
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.