Calculus of Variations and Geometric Measure Theory

F. Santambrogio

Sharp Wasserstein estimates for integral sampling and Lorentz summability of transport densities

created by santambro on 28 Feb 2022
modified on 17 Nov 2022


Accepted Paper

Inserted: 28 feb 2022
Last Updated: 17 nov 2022

Journal: J. Funct. An.
Year: 2022

This paper is an answer to a conjecture in https:/arxiv.orgabs2010.12946


We prove some Lorentz-type estimates for the average in time of suitable geodesic interpolations of probability measures, obtaining as a by product a new estimate for transport densities and a new integral inequality in terms of Wasserstein distances and norms of gradients. This last inequality was conjectured in a paper by S. Steinerberger.