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Ufimsk. Mat. Zh., 2010, Volume 2, Issue 3, Pages 31–38 (Mi ufa60)  

This article is cited in 2 scientific papers (total in 2 papers)

Three equivalent hypotheses on estimation of integrals

R. A. Baladai, B. N. Khabibullin

Bashkir State University, Ufa, Russia

Abstract: We offer a hypothesis on precise estimation of a definite improper integral depending on a parameter $\lambda\in(0,+\infty)$ by means of a given estimation of another definite integral depending on parameters $t\in[0,+\infty)$ and $\lambda$. This precise estimation is proved for $\lambda\leq1$. Besides, an exact estimation is obtained for $\lambda>1$. The later estimation does not seem to be exact. We give two more hypotheses that are equivalent to the original one. Our conjectures originated from extreme problems for entire, meromorphic, and plurisubharmonic functions of several variables.

Keywords: improper integral, estimate, inequality, entire function, meromorphic function, plurisubharmonic function, Paley problem.

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Bibliographic databases:

Document Type: Article
UDC: 517.16+517.574+517.555
Received: 15.06.2010

Citation: R. A. Baladai, B. N. Khabibullin, “Three equivalent hypotheses on estimation of integrals”, Ufimsk. Mat. Zh., 2:3 (2010), 31–38

Citation in format AMSBIB
\Bibitem{BalKha10}
\by R.~A.~Baladai, B.~N.~Khabibullin
\paper Three equivalent hypotheses on estimation of integrals
\jour Ufimsk. Mat. Zh.
\yr 2010
\vol 2
\issue 3
\pages 31--38
\mathnet{http://mi.mathnet.ru/ufa60}
\zmath{https://zbmath.org/?q=an:1240.32033}
\elib{http://elibrary.ru/item.asp?id=15240753}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ufa Math. J., 10:3 (2018), 117–130  mathnet  crossref
    2. A. Bërdëllima, “A note on a conjecture by Khabibullin”, Issledovaniya po lineinym operatoram i teorii funktsii. 46, Zap. nauchn. sem. POMI, 467, POMI, SPb., 2018, 7–20  mathnet
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