ShowMe Analysis Meeting 2004 June 3-5, 2004 University of Missouri Columbia, Missouri

Donald Burkholder (University of Illinois)
Searching for the best when the good is not good enough

Abstract: Even though most inequalities in analysis need not be provided with the best possible constants to be useful, some of the inequalities gain in their usefulness if so provided. If this is the case or not, they can often be much better understood if conceptually simple proofs are discovered that yield the best possible constants. We shall review some old and give some new examples of this in the setting of martingale theory and harmonic analysis, and also mention some open problems. In this talk, only elementary probability tools will be needed.