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L ∞ Norm Estimation of Interpolations on the Heisenberg Group(PDF)

《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

Issue:
2020年02期
Page:
6-9
Research Field:
·数学·
Publishing date:

Info

Title:
L ∞ Norm Estimation of Interpolations on the Heisenberg Group
Author(s):
Chen Ping
School of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,China
Keywords:
Heisenberg group; interpolation; L∞ norm estimation
PACS:
-
DOI:
10.3969/j.issn.1001-4616.2020.02.002
Abstract:
In this paper,we discuss the interpolation μt of optimal transport plan γ in the Heisenberg group(Hn,d,L2n+1)with the cost function (d(x,y))where is a strictly convex function. An interpolation is actually a kind of measure. We show that the interpolation μt is absolutely continuous with respect to the Lebsegue measure L2n+1. We also give a L∞ norm estimation on μt. Furthermore,as a corollary of the above estimation result,we also estimate the interpolation(etS)#γε of solutions of the variational approximation problem in the Heisenberg group. The main methods we used include the L2n+1 measure contraction property of the Heisenberg group,the cyclically monotonicity in the optimal transport theory and the strictly convexity of .

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Last Update: 2020-05-15