PSEUDO-DIFFERENTIAL OPERATOR]{THE PSEUDO-DIFFERENTIAL OPERATOR ON LOCAL HARDY MORREY SPACE

Abstract

The main purpose of this paper is to prove the boundedness of pseudo-differential operators with symbols in $S_{1, \delta}^{-\alpha}$ from one local Hardy Morrey space to another one by using the atomic decomposition. To overcome the essential difficulty caused by the absence of absolute continuity of quasi-norm in Morrey spaces, the most novelty of the paper exists in that Morrey space is embedded into the weighted Lebesgue space with certain special weight to control the convergence of the sum in the decomposition.