Email this article On local equivalence of the majorant of partial sums and Paley function of Franklin series
- Authors: Gevorkyan G.G.1, Keryan K.A.1
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Affiliations:
- Yerevan State University
- Issue: Vol 52, No 1 (2017)
- Pages: 38-47
- Section: Real and Complex Analysis
- URL: https://journals.rcsi.science/1068-3623/article/view/227998
- DOI: https://doi.org/10.3103/S1068362317010058
- ID: 227998
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Abstract
In this paper we prove that the majorant of partial sums and the Paley function of Franklin series have equivalent norms in the space Lp(I), p > 0, provided that the “peak” intervals of Franklin functions with non-vanishing coefficients lie in I. Examples of series emphasizing that this condition is essential are also given.
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About the authors
G. G. Gevorkyan
Yerevan State University
Author for correspondence.
Email: ggg@ysu.am
Armenia, Yerevan
K. A. Keryan
Yerevan State University
Email: ggg@ysu.am
Armenia, Yerevan
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