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 (Formula Presented) where U, V ⊂ R n are 0-symmetric convex bodies and f is a non-negative positive definite function. © 2018 American Mathematical Society.