scholarly journals On Weighted Integrability of Functions Defined by Trigonometric Series

2010 ◽  
Vol 2010 (1) ◽  
pp. 485705 ◽  
Author(s):  
Bogdan Szal
Keyword(s):  
Trigonometric Series ◽  
Integrability Of Functions ◽  
Weighted Integrability

scholarly journals On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Bogdan Szal ◽  
Maciej Kubiak
Keyword(s):  
Trigonometric Series ◽  
Bounded Variation ◽  
Necessary Condition ◽  
Integrability Of Functions ◽  
Sufficient And Necessary Condition ◽  
Weighted Integrability

Abstract In this paper we introduce new classes of p-bounded variation sequences and give a sufficient and necessary condition for weighted integrability of trigonometric series with coefficients belonging to these classes. This is a generalization of the results obtained by the first author [J. Inequal. Appl. 2010:1–19, 2010] and Dyachenko and Tikhonov [Stud. Math. 193(3):285–306, 2009].

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