Reaching L^1 via Extrapolation Theory

Analysis Seminar
Wednesday, April 8, 2015 - 2:05pm for 1 hour (actually 50 minutes)
Skiles 005
Carlos Domingo – University of Barcelona
Michael Lacey
The classical Rubio de Francia extrapolation allows you to obtain strong-type estimates for weights in A_p (and every p>1) if you can show that it holds for some p_0>1. However, the endpoint p=1 has to be treated separately. In this talk we will explain how to deduce weak-type (1,1) estimates for A_1 weights if we have a certain restricted weak-type inequality at some level p_0>1. We will then show how this approach can be applied to the Bochner-Riesz operator at the critical index and Fourier multipliers.