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Khabibullin's conjecture on integral inequalities
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Khabibullin's conjecture on integral inequalities : ウィキペディア英語版
Khabibullin's conjecture on integral inequalities

In mathematics, Khabibullin's conjecture, named after B. N. Khabibullin, is related to Paley's problem for plurisubharmonic functions and to various extremal problems in the theory of entire functions of several variables.
== The first statement in terms of logarithmically convex functions ==
Khabibullin's conjecture (version 1, 1992). ''Let \displaystyle S be a non-negative increasing function on the half-line [0,+\infty) such that \displaystyle S(0)=0. Assume that \displaystyle S(e^x) is a convex function of x\in[-\infty,+\infty). Let \lambda\geq 1/2, n\geq 2, and n\in\mathbb N. If''
''then''
\,dt\leq \frac\prod_^ \Bigl(1+\frac\Bigr).|}}
This statement of the Khabibullin's conjecture completes his survey.

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