Abstract

In real Hardy spaces $H^p({\mathbb{R}}^n)$ for , to check whether a singular integral operator $T$ is bounded on $H^p({\mathbb{R}}^n)$, it is common to show that $T(a)$ is a molecule with the assumption that $T^{\ast }(1)=0$. In this talk, we consider a similar situation in the local Hardy spaces $h^p({\mathbb{R}}^n)$, with a broader class of molecules defined by a weaker cancellation condition. Moreover, we will discuss the properties of the singular integral operator if it maps atoms to molecules. This talk is based on the papers with Galia Dafni, Tiago Picon, and Claudio Vasconcelos.

Zoom Link

https://us02web.zoom.us/j/87303952902

Organizer

Daniel Spector (NTNU)