Functional Inequalities for Convolution Probability Measures

الأصل · EN

Let μ and ν be two probability measures on ᵈ, where μ(x)= ⁻ᵛ⁽ˣ⁾ x for some V∈ C¹(ᵈ). Explicit sufficient conditions on V and ν are presented such that μ*ν satisfies the log-Sobolev, Poincaré and super Poincaré inequalities. In particular, the recent results on the log-Sobolev inequality derived in Z for convolutions of the Gaussian measure and compactly supported probability measures are improved and extended.