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