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

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.

9 pages

References in corpus (1)

• On integral estimates of non-negative positive definite functions