University of Toronto
                   PDE/Applied Math/Analysis Seminar
                     Friday 30. May 2008, 2:10-3pm
                           6183 Bahen Center

                    *** please note unusual hour ***



SPEAKER:  Stefan Valdimarsson (UCLA)

TITLE:    Multilinear fractional integration and Hilbert transform

ABSTRACT: We will look at certain multilinear gerneralizations of
           fractional integration and the Hilbert transfrom. We will
           discuss motivations and previous work in this area. Geometric
           invariances play a big role and allow the operators to be
           defined on Euclidean space, the sphere and hyperbolic
           space. We will demonstrate how to prove L^p boundedness
           of the Hilbert transform variant and discuss issues that
           arise with the definition.

           For the fractional integration variant, we will locate the
           best constant for the L^p boundedness inequality in the
           case with most symmetries and determine the functions
           which furnish it. For this we will need to discuss
           symmetrization inequalities and cases of equality for them.



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University of Toronto PDE/Applied Math/Analysis Seminar 
http://www.math.toronto.edu/appmath/

2007-2008 organizers:
           Walid Abou-Salem     walid@ math.toronto.edu
           Almut Burchard       almut@ math.toronto.edu
           Robert McCann        mccann@ math.toronto.edu
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