Extrapolation of Carleson measures

Series: 
Analysis Seminar
Monday, April 5, 2010 - 13:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
University of Missouri
Organizer: 
We discuss joint work with J.-M. Martell, in which werevisit the ``extrapolation method" for Carleson measures, originallyintroduced by John Lewis to proveA_\infty estimates for certain caloric measures, and we present a purely real variable version of the method.  Our main result is a general criterion fordeducing that a weight satisfies a ReverseHolder estimate, given appropriate control by a Carleson measure.To illustrate the useof this technique,we reprove a well known theorem of R. Fefferman, Kenig and Pipherconcerning the solvability of the Dirichlet problem with data in some L^p space.