Abstract:
In this paper, we study the integrability of optimal mappings $T$ taking a probability measure
$\mu$ to another measure $g\cdot\mu$. We assume that $T$ minimizes the cost function $c$
and $\mu$ satisfies some special inequalities related to $c$ (the infimum-convolution inequality or the logarithmic $c$-Sobolev inequality). The results obtained are applied to the analysis of measures of the form $\exp(-|x|^{\alpha})$.
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