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arXiv · 1612.08637

Doubling condition at the origin for non-negative positive definite functions

Dmitry Gorbachev·Sergey Tikhonov
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Abstract

We study upper and lower estimates as well as the asymptotic behavior of the sharp constant $C=C_n(U,V)$ in the doubling-type condition at the origin \[ \frac{1}{|V|}\int_{V}f(x)\,dx\le C\,\frac{1}{|U|}\int_{U}f(x)\,dx, \] where $U,V\subset \mathbb{R}^{n}$ are $0$-symmetric convex bodies and $f$ is a non-negative positive definite function.

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Dmitry Gorbachev, Sergey Tikhonov. 2016-12-27. Doubling condition at the origin for non-negative positive definite functions. https://arxiv.org/abs/1612.08637

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