Fu Jen lectures in Hardy spaces

In this paper, we survey some multiplier theorems and their applications to estimates for wave equation in Hardy spaces HP(R-n). We also prove H-p bou ndedness for Calderon-Zygmund operators of type sigma which can be consider ed as a generalization of classical singular integral operators. Using thes e results, we discuss some recent progress in H-p regularity properties of the solving operators for hyperbolic, equations.