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Home » Harmonic Analysis Seminar: Convex body domination and theory of A_p matrix weights revisited

Seminar

Harmonic Analysis Seminar: Convex body domination and theory of A_p matrix weights revisited March 01, 2017 (02:00 PM PST - 03:00 PM PST)
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Location: MSRI: Simons Auditorium
Speaker(s) Sergei Treil (Brown University)
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After describing some motivations for  weighted estimates of singular integral operators with matrix weights, I'll discuss the method of estimating vector-valued singular integral operators by the so called sparse operators. In the scalar case the sparse domination is a recently introduced powerful tool of harmonic analysis, and generalizing it to the vector valued case helps in many problems. 

Of course, trivial generalization does not work: the target space of our sparse operator is the set of convex-body-valued functions. It looks complicated, but the weighted estimated of such operators is an easy task. As an application we get a new easy proof of the weighted estimates of the vector Calderon-Zygmund operators with matrix Muckenhoupt weights. 

Some intriguing open problems will also be discussed. 

The talk is partially based on a joint work with F. Nazarov, S. Petermichl and A. Volberg.

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