We discuss some refinements of the classical Prekopa-Leindler inequality, which consist in the addition of an extra-term depending on a distance modulo translations. Our results hold true on suitable classes of functions of n variables. They are based upon two different kinds of 1-dimensional refinements: the former is the one obtained by K. M. Ball and K. Boroczky in [4] and involves an L-1-type distance on log-concave functions, the latter is new and involves the transport map onto the Lebesgue measure. Starting from each of these 1-dimensional refinements, we obtain an n-dimensional counterpart by exploiting a generalized version of the Cramer-Wold Theorem.
Lower bounds for the Prékopa-Leindler deficit by some distances modulo translations
FRAGALÀ, ILARIA MARIA RITA
2014-01-01
Abstract
We discuss some refinements of the classical Prekopa-Leindler inequality, which consist in the addition of an extra-term depending on a distance modulo translations. Our results hold true on suitable classes of functions of n variables. They are based upon two different kinds of 1-dimensional refinements: the former is the one obtained by K. M. Ball and K. Boroczky in [4] and involves an L-1-type distance on log-concave functions, the latter is new and involves the transport map onto the Lebesgue measure. Starting from each of these 1-dimensional refinements, we obtain an n-dimensional counterpart by exploiting a generalized version of the Cramer-Wold Theorem.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
