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

Gorbachev, Dmitry; Tikhonov, Sergey

doi:10.1090/proc/14191

Doubling condition at the origin for non-negative positive definite functions
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by Dmitry Gorbachev and Sergey Tikhonov PDF

Proc. Amer. Math. Soc. 147 (2019), 609-618 Request permission

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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