Summability of multiple Fourier series. Growth of Lebesgue constants

1980 ◽  
Vol 6 (3) ◽  
pp. 255-267 ◽  
Author(s):  
Р. М. тРИгУБ
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series ◽  
Lebesgue Constants

On the absolute convergence of multiple fourier series

2007 ◽  
Vol 117 (3) ◽  
pp. 275-292 ◽  
Author(s):  
Ferenc Móricz ◽  
Antal Veres
Keyword(s):  
Fourier Series ◽  
Absolute Convergence ◽  
Multiple Fourier Series ◽  
The Absolute

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.

scholarly journals An example of Torrigiani related to multiple Fourier series.

1972 ◽  
Vol 19 (3) ◽  
pp. 285-287 ◽  
Author(s):  
Casper Goffman
Keyword(s):  
Fourier Series ◽  
Multiple Fourier Series
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