T1 Theorem and local Tb Theorems for Square functions

Saturday, June 2, 2012 - 11:00am - 11:30am
Keller 3-180
The Tb theorem, like its predecessor, the T1 Theorem,
is a an L^2 boundedness criterion, originally established by McIntosh
and Meyer, and by David, Journe and Semmes in the context of singular
integrals, but later extended by Semmes to the setting of “square
functions”. The latter arise in many applications in complex function
theory and in PDE, and may be viewed as singular integrals taking values
in a Hilbert space. The essential idea of Tb and T1 type theorems, is that
they reduce the question of L^2 boundedness to verifying the behavior of
an operator on a single test function b (or even the constant function 1).
The point is that sometimes particular properties of the operator may be
exploited to verify the appropriate testing criterion.

In particular, during the talk I would present some results
for square functions with non-pointwise bounded kernels as well
as the motivation that leads us to study such case. The work presented
is a joint work with prof. Steve Hofmann.
MSC Code: