A simple(?) geometric or combinatorial question with deep consequences for BMO functions

Tuesday, April 12, 2016 - 2:00pm
Math Sci 111
Michael Cwikel
(Technion - Israel Institute of Technology)

Most of the work to be described in this talk is joint with Yoram
Sagher and Pavel Shvartsman and appeared in our joint paper of 2012.
I will pose and invite you to solve a seemingly rather simple
geometric/combinatorial question.
In fact I will formulate a slightly simpler equivalent and so far
unpublished variant of the question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 briefly describe BMO, and mention
some of its remarkable properties and connections with harmonic
analysis and complex analysis. 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.
Various relevant links and additional material about this research
are available at

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