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

2016/12/27 by Д. В. Горбачев, Sergey Tikhonov, Gorbachev, Dmitry +1
Mathematics · #42A38 #42A82 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1612.08637

openalex publication_date 2016/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study upper and lower estimates as well as the asymptotic behavior of the\nsharp constant C=C_n(U,V) in the doubling-type condition at the origin n
frac1|V|
int_Vf(x)
,dx
le C
,
frac1|U|
int_Uf(x)
,dx, where\nU,V\⊂ \ℝⁿ are 0-symmetric convex bodies and f is a\nnon-negative positive definite function.\n

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