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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2012, Number 8, Pages 15–26 (Mi ivm8727)  
The weighted $L^1$-integrability of functions and the Parseval equality with respect to multiplicative systems

S. S. Volosivets

Chair of Function Theory and Approximation, Saratov State University, Saratov, Russia
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Abstract: In this paper we prove necessary and sufficient conditions for the weighted $L^1$-integrability of functions defined on $[0,1)$ in terms of Fourier coefficients with respect to a multiplicative system of bounded type. These results are counterparts of trigonometric ones by M. and S. Izumi and M. M. Robertson.
Keywords: multiplicative systems of bounded type, weighted $L^1$-integrability, generalized monotonicity.
Received: 07.07.2011
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2012, Volume 56, Issue 8, Pages 11–21
DOI: https://doi.org/10.3103/S1066369X12080026
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: S. S. Volosivets, “The weighted $L^1$-integrability of functions and the Parseval equality with respect to multiplicative systems”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 8, 15–26; Russian Math. (Iz. VUZ), 56:8 (2012), 11–21
Citation in format AMSBIB
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\by S.~S.~Volosivets
\paper The weighted $L^1$-integrability of functions and the Parseval equality with respect to multiplicative systems
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2012
\issue 8
\pages 15--26
\mathnet{http://mi.mathnet.ru/ivm8727}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3077483}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2012
\vol 56
\issue 8
\pages 11--21
\crossref{https://doi.org/10.3103/S1066369X12080026}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866257012}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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