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Lp,q Estimation of a Transport Density(PDF)

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

Issue:
2022年01期
Page:
8-11
Research Field:
·数学·
Publishing date:

Info

Title:
Lp,q Estimation of a Transport Density
Author(s):
Chen Ping
(School of Mathematics and Information Technology,Jiangsu Second Normal University,Nanjing 210013,China)
Keywords:
Lp; q estimate; transport density; displacement interpolations
PACS:
O186.14
DOI:
10.3969/j.issn.1001-4616.2022.01.002
Abstract:
The paper presents the absolute continuity and Lp,q summability of a transport density σγ associated to an optimal transport plan γ between two probability measures μ and v. More precisely,σγ∈Lp,q holds if μ∈Lp,q where 1≤p<+∞,1≤q<+∞ and v has a finite support set. The main methods we used include the equivalent redefinition of σγ by displacement interpolations μt,the relationship inequality between σγ and μt,and the Lp,q estimation of such interpolations μt.

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