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- Publisher
- Springer International Publishing
- Copyright
- © Springer Nature Switzerland AG 2019
- ISBN
- 978-3-030-26390-4
- Pages
- 71 –97
- DOI
- 10.1007/978-3-030-26391-1_7
- Publisher site
- See Chapter on Publisher Site
Abstract
[We investigate the interactions of functional rearrangements with Prékopa–Leindler type inequalities. It is shown that certain set theoretic rearrangement inequalities can be lifted to functional analogs, thus demonstrating that several important integral inequalities tighten on functional rearrangement about “isoperimetric” sets with respect to a relevant measure. Applications to the Borell–Brascamp–Lieb, Borell–Ehrhard, and the recent polar Prékopa–Leindler inequalities are demonstrated. It is also proven that an integrated form of the Gaussian log-Sobolev inequality sharpens on rearrangement.]
Published: Nov 27, 2019