Sharp constants for composition with a bi-Lipschitz measure-preserving map

Frederic Bernicot (1) , Sahbi Keraani (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 LPP - Laboratoire Paul Painlevé - UMR 8524

In this note, we aim to describe sharp constants for the composition operator with a bi-Lipschitz measure-preserving map in several functional spaces (BMO, Hardy space, Carleson measures, ...). It is interesting to see how the measure preserving property allows us to improve these constants. Moreover, we will prove the optimality of our results for the BMO space and describe improved estimates for solutions of transport PDEs.

Mots clés: BMO space; Composition; Measure-preserving map

Domaines: Analyse classique [math.CA]

Frederic Bernicot, Sahbi Keraani. Sharp constants for composition with a bi-Lipschitz measure-preserving map. Mathematical Research Letters, 2014, 21, pp.937-952. ⟨hal-00691533⟩