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

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. Ine...

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Main Authors:	Bogdan Szal, Maciej Kubiak
Format:	Article
Language:	English
Published:	SpringerOpen 2019-10-01
Series:	Journal of Inequalities and Applications
Subjects:	Trigonometric series Sequences of p-bounded variation Weighted L p $L^{p}$ integrability
Online Access:	http://link.springer.com/article/10.1186/s13660-019-2225-1

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spelling	doaj-ddd141e41f954d37b6ebef0b0c16b6cd2020-11-25T04:02:57ZengSpringerOpenJournal of Inequalities and Applications1029-242X2019-10-012019111810.1186/s13660-019-2225-1On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficientsBogdan Szal0Maciej Kubiak1Faculty of Mathematics, Computer Science and Econometrics, University of Zielona GóraFaculty of Mathematics, Computer Science and Econometrics, University of Zielona GóraAbstract 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].http://link.springer.com/article/10.1186/s13660-019-2225-1Trigonometric seriesSequences of p-bounded variationWeighted L p $L^{p}$ integrability
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Bogdan Szal Maciej Kubiak
spellingShingle	Bogdan Szal Maciej Kubiak On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients Journal of Inequalities and Applications Trigonometric series Sequences of p-bounded variation Weighted L p $L^{p}$ integrability
author_facet	Bogdan Szal Maciej Kubiak
author_sort	Bogdan Szal
title	On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
title_short	On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
title_full	On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
title_fullStr	On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
title_full_unstemmed	On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
title_sort	on weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2019-10-01
description	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].
topic	Trigonometric series Sequences of p-bounded variation Weighted L p $L^{p}$ integrability
url	http://link.springer.com/article/10.1186/s13660-019-2225-1
work_keys_str_mv	AT bogdanszal onweightedintegrabilityoffunctionsdefinedbytrigonometricserieswithpboundedvariationcoefficients AT maciejkubiak onweightedintegrabilityoffunctionsdefinedbytrigonometricserieswithpboundedvariationcoefficients
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On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients

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