Conditions for the localization of partial sums of S. M. Nikol'skii's class of multiple trigonometric Fourier series

1970 ◽  
Vol 8 (5) ◽  
pp. 803-809
Author(s):  
V. A. Il'in
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Partial Sums ◽  
Multiple Trigonometric Fourier Series

scholarly journals The multipliers of multiple trigonometric Fourier series

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
Aizhan Ydyrys ◽  
Lyazzat Sarybekova ◽  
Nazerke Tleukhanova
Keyword(s):  
Fourier Series ◽  
Sufficient Conditions ◽  
Regular System ◽  
Multiple Fourier Series ◽  
Trigonometric Fourier Series ◽  
Lorentz Spaces ◽  
Complex Numbers ◽  
Multiple Trigonometric Fourier Series

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.

On the Exponential Uniform Strong Summability of Multiple Trigonometric Fourier Series

2009 ◽  
Vol 16 (3) ◽  
pp. 517-532
Author(s):  
Larry Gogoladze
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Strong Summability ◽  
Multiple Trigonometric Fourier Series

Abstract In the paper, in particular, it is proved that the 𝑠-dimensional trigonometric Fourier series of the 2π-periodic continuous on [–π, π]𝑠 function 𝑓 is uniformly strong summable to the function 𝑓 exponentially in the power . Moreover, it is proved that this result is best possible.

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