Tel-Aviv University
School of Mathematical Sciences
Department Colloquium
Monday, March 14, 2011
Schreiber 006, 12:15
Michael Cwikel
Technion, Israel Institute of Technology
A simple(?) geometric question with deep consequences for BMO functions.
Abstract: I will pose and invite you to solve a seemingly rather simple geometric/combinatoric question.
My coauthors and I have discovered that an affirmative answer to this question would have some very interesting consequences in analysis. They relate to the very important function space BMO (of functions of Bounded Mean Oscillation). I will not assume familiarity with BMO, and will briefly survey some of its remarkable properties.
Special cases of one of our results give alternative proofs of the celebrated John-Nirenberg inequality for BMO functions. An affirmative answer to the above-mentioned question would lead to a version of the John-Nirenberg inequality with dimension free constants.
A more extensive version of this abstract and a first version of our detailed paper etc. are available at
http://www.math.technion.ac.il/~mcwikel/bmo
This is joint work with Yoram Sagher and Pavel Shvartsman.
