Mathematical Research Letters

Volume 21 (2014)

Number 5

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

Pages: 937 – 952



Frédéric Bernicot (CNRS, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France)

Sahbi Keraani (UFR de Mathématiques, Université de Lille 1, Villeneuve d’Ascq, France)


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, etc.). 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.


BMO space, composition, measure-preserving map

2010 Mathematics Subject Classification

42B25, 42B35

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