Sharp maximal function estimates and $H^p$ continuities of pseudo-differential operators

Abstract

It is studied that pointwise estimates and continuities on Hardy spaces of pseudo-differential operators (PDOs for short) with the symbol in general Hörmander's classes. We get weighted weak-type $(1,1)$ estimate, weighted normal inequalities, $(H^p,H^p)$ continuities and $(H^p,L^p)$ continuities for PDOs, where $0<p\le 1$.