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 H\"{o}rmander'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 $0<p\leq1$.