scholarly journals Equiconvergence of expansions in multiple trigonometric Fourier series and Fourier integral with "Jk-lacunary sequences of rectangular partial sums"

2014 ◽  
Vol 18 (1) ◽  
pp. 69 ◽  
Author(s):  
Igor L. Bloshanskii ◽  
Denis A. Grafov
Keyword(s):  
Fourier Series ◽  
Fourier Integral ◽  
Trigonometric Fourier Series ◽  
Partial Sums ◽  
Lacunary Sequences ◽  
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.

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