Pseudodifferential operators on local Hardy spaces (Q1027730)

The authors study the boundedness of the pseudo-differential operators on the local Hardy spaces \(h^p(\mathbb{R}^n)\), \(0<p\leq 1\), defined as in \textit{D. Goldberg} [Duke Math. J., 46, 27--42 (1979; Zbl 0409.46060)]. The obtained results are very general, and include the class of the operators with symbol in \(S^0_{1,\delta}(\mathbb{R}^n)\), \(0\leq\delta<1\), the paradifferential operators of \textit{J. M. Bony} [Ann. Sci. Éc. Norm. Supér., 14, 209--246 (1981; Zbl 0495.35024)] as well as other subclasses of \(S^0_{1,1}(\mathbb{R}^n)\). An application is given to the local solvability of the complex vector field \(L=\partial_t+ib(x,t) \partial_x\) in spaces of Hardy type.