Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets

Anat Amir

doi:10.3934/era.2011.18.61

Article Contents

2011, Volume 18: 61-68. Doi: 10.3934/era.2011.18.61

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Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets

Anat Amir^1,

1.
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978

Received: January 31, 2011

Revised: April 30, 2011

Published: December 2010

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Abstract

Zapolsky's inequality gives a lower bound for the $L_1$ norm of the Poisson bracket of a pair of $C^1$ functions on the two-dimensional sphere by means of quasi-states. Here we show that this lower bound is sharp.

Keywords:

Quasi-state.

Mathematics Subject Classification: Primary: 53D99.

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References

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