This article is cited 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.

UDC: 517.16+517.574+517.555

Received: 15.06.2010

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