University of Toronto
                  PDE/Applied Math/Analysis Seminar
                  Friday 4. April, 1:10-2:00pm
                          6183 Bahen Center      



SPEAKER:  Carlo Morpurgo (University of Missouri, Columbia)

TITLE:    Sharp Moser-Trudinger and Beckner-Onofri's inequalities 
          on the CR sphere

ABSTRACT: The classical Moser-Trudinger inequality represents 
          the imbedding of the Sobolev space W^{n/p,p} into an 
          exponential class, where n is the dimension of the 
          ambient space. The sharp form of this inequality is 
          known for domains of R^n and for compact Riemannian 
          manifolds.  When p=2 another sharp form of the imbedding 
          can be given via the so-called Onofri-Beckner type 
          estimate, which was first derived by Onofri on S^2 and 
          later discovered by Beckner in the general n-dimensional 
          setting. The derivatives are controlled by the 
          intertwining operator of order n, also known as the 
          Paneitz operator, which makes the inequality invariant 
          under the conformal group. In this talk I will present 
          some natural versions of the above results on the 
          complex sphere S^{2n+1}. Adams type inequalities on 
          measure spaces will also be briefly  discussed.  
	  


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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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