# American Institute of Mathematical Sciences

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

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

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

Received  February 2011 Revised  May 2011 Published  July 2011

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.
Citation: Anat Amir. Sharpness of Zapolsky's inequality for quasi-states and Poisson brackets. Electronic Research Announcements, 2011, 18: 61-68. doi: 10.3934/era.2011.18.61
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