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MIGSAA mini-course in harmonic analysis by Professor Arpad Benyi

A new MIGSAA short course in harmonic analysis is taking place 21st and 22nd April in University of Edinburgh.

Title: 'Smoothing of commutators for certain classes of bilinear operators'

When: 3 pm - 5 pm on Thursday 21st and Friday 22nd April 2016

Where: James Clerk Maxwell Building, room 6206, University of Edinburgh

The course is given by Professor Arpad Benyi of Western Washington University whose main area of research lies at the interface of Fourier analysis, operator theory and partial differential equations.

Abstract: We will begin by reviewing, in linear setting, some basic facts about Calderon-Zygmund operators, Muckenhoupt weights and the classical result of Coifman-Rochberg-Weiss about the commutator of the Hilbert transform and BMO. We will then move on to the bilinear setting.

After stating some known facts about the corresponding objects in this theory, we will explore the smoothing effect of commutators of certain classes of bilinear operators and functions in appropriate spaces. In particular, with (p, q, r) a Holder triple, we will prove the (weighted) L^p x L^q -> L^r compactness of commutators of bilinear Calderon-Zygmund operators with functions of continuous mean oscillation as well as the L^p x L^q -> L^r boundedness of commutators of classes of bilinear pseudodifferential operators that fall outside the Calderon-Zygmund theory with Lipschitz functions.