Sobolev inequalities for harmonic measures on spheres

Jing Du, Liangzhen Lei and Yutao Ma

Statistics & Probability Letters, 2015, vol. 100, issue C, 104-114

Abstract: In this paper, we consider the harmonic measure on the unit sphere Sn−1 on Rn (n≥2) and offer a two-sided estimate of precise order on the Sobolev constant with exponent p∈(1,2). As special cases for p=1 and p tending to 2, our estimates recover those in Barthe et al. (2104) for n≥3 and in Ma and Zhang (2014) for n=2.

Keywords: Harmonic measures; Unit spheres; Sobolev inequalities; Poincaré inequalities; Logarithmic Sobolev inequalities (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1016/j.spl.2015.02.008

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