LetL=L0+VbethehigherorderSchrdigertypeoperatorwhereL0isahomogeneousellipticoperatoroforder2minpergenceformwithboundedcoefficientsandVisarealmeasurablefunctionasmultiplicationoperator(e.g.,including(-?)m+V(m∈N)asspecialexamples).Inthispaper,assumethatVsatisfiesastronglysubcriticalformconditionassociatedwithL0,theauthorsattempttoestablishatheoryofHardyspaceHpL(Rn)(0