Uchiyama's lemma and the John-Nirenberg inequality

Analysis Seminar
Wednesday, August 29, 2012 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
University of Alabama
Using integral formulas based on Green's theorem and in particular a lemma of Uchiyama, we give simple proofs of comparisons of different BMO norms without using the John-Nirenberg inequality while we also give a simple proof of the strong John-Nirenberg inequality. Along the way we prove the inclusions of BMOA in the dual of H^1 and BMO in the dual of real H^1. Some difficulties of the method and possible future directions to take it will be suggested at the end.