Pseudodifferential Operators on Local Hardy Spaces

In this work, we study the continuity of pseudodifferential operators on local Hardy spaces hp(ℝn) and generalize the results due to Goldberg and Taylor by showing that operators with symbols in S1,δ0(ℝn), 0≤δ<1, and in some subclasses of S1,10(ℝn) are bounded on hp(ℝn) (0<p≤1). As an application, we study the local solvability of the planar vector field L=∂t+ib(x,t)∂x, b(x,t)≥0, in spaces of mixed norm involving Hardy spaces.