Introduction Program Talks & posters Participants Practical Info
Young Women in Harmonic Analysis and PDE
December 2-4, 2016
Stefanie Petermichl (Université Paul Sabatier)
Characterizations of multi-parameter BMO spaces through boundedness of commutators
The characterisation of symbols that result in bounded Hankel or
Toeplitz operators are classical and rather simple. When passing to
real analysis and notably to multi-parameter real analysis, these
questions become very quickly interesting and intensely complicated.
We discuss the simplicity and beauty of the classical base cases as
well as the cornerstones into the world of real analysis 'away' from
operator theory. In this situation one studies 'commutators' the
simplest one of which takes the form
$$Hb-bH$$
where $H$ is the Hilbert transform and $b$ stands for multiplication by a
(bmo) function. Multi-parameter study of related objects was initiated
by Sarah Ferguson and Cora Sadosky in the late 90s.
The real variable one-parameter theory we discuss includes parts of a
classical article by Coifman Rochberg Weiss while the multi-parameter
questions include a deep line by Ferguson, Lacey, Pipher, Wick, myself
and others.
Emphasis is given to a recent result by Ou, Strouse and myself that
solves an endpoint question begun by Ferguson/Sadosky. Although the
proofs are 'hard analysis' exploiting several recent developments, one
recognises the core that lies in elegant arguments stemming from
operator theory.
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