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

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

2012-04-26

arxiv.org/abs/1204.6008v1

Mathematics

Classical Analysis and ODEs

12 pages

Scientific paper

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.

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