Weighted estimates for Beltrami operators


Albert Clop,


(Universitat Autonoma de Barcelona)


Jueves 15 de noviembre 2012



While studying inhomogeneous, degenerate Beltrami equations, the following question arises in a natural way: what are the weights \omega such that any Beltrami diferential operator dominates the full differential in the L^p(\omega) norm? In the Cauchy-Riemann setting, we know that the answer is given by the class of Muckenhoupt weights. Unfortunately, for a general Beltrami operators the situation might be different. We will give some partial answers. We will also comment on some connections with quasiconformality, and finally we will pose some open problems.