Almost Everywhere Convergence of Multiple Trigonometric Fourier Series of Functions from Sobolev Classes

2021 ◽  
Vol 109 (1-2) ◽  
pp. 157-162
Author(s):  
R. R. Ashurov
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Sobolev Classes ◽  
Almost Everywhere Convergence ◽  
Multiple Trigonometric Fourier Series ◽  
Almost Everywhere ◽  
Series Of Functions

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.

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