Parabolic Singular Integrals on Ahlfors Regular Sets

Abstract

We present a survey of recent developments on a parabolic version of uniform rectifiability and parabolic singular integrals. In particular we describe some ideas to prove the equivalence between the parabolic uniform rectifiability of a set $E$ and the $L^2(E)$ boundedness of a class of Calder´on Zygmund integrals of parabolic type. We also describe a result on compactness of certain parabolic singular integrals, as well as some related open problems and conjectures.