A necessary condition for uniform convergence of double sine series with $p$-bounded variation coefficients

2021 ◽  
Author(s):  
Mateusz Kubiak ◽  
Bogdan Szal
Keyword(s):  
Uniform Convergence ◽  
Bounded Variation ◽  
Necessary Condition ◽  
Sine Series

scholarly journals On the uniform convergence of double sine series

2009 ◽  
Vol 193 (1) ◽  
pp. 79-97 ◽  
Author(s):  
Péter Kórus ◽  
Ferenc Móricz
Keyword(s):  
Uniform Convergence ◽  
Sine Series

scholarly journals L1-convergence of double trigonometric series

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3759-3771
Author(s):  
Karanvir Singh ◽  
Kanak Modi
Keyword(s):  
Trigonometric Series ◽  
Bounded Variation ◽  
Pointwise Convergence ◽  
Null Sequence ◽  
Sine Series ◽  
Double Trigonometric Series ◽  
L1 Norm ◽  
Cosine Series

In this paper we study the pointwise convergence and convergence in L1-norm of double trigonometric series whose coefficients form a null sequence of bounded variation of order (p,0),(0,p) and (p,p) with the weight (jk)p-1 for some integer p > 1. The double trigonometric series in this paper represents double cosine series, double sine series and double cosine sine series. Our results extend the results of Young [9], Kolmogorov [4] in the sense of single trigonometric series to double trigonometric series and of M?ricz [6,7] in the sense of higher values of p.

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