The continuity of pseudo-differential operators on weighted local Hardy spaces
Volume 198 / 2010
Studia Mathematica 198 (2010), 69-77
MSC: 42B20, 47G30.
DOI: 10.4064/sm198-1-4
Abstract
We first show that a linear operator which is bounded on $L^2_w$ with $w\in A_1$ can be extended to a bounded operator on the weighted local Hardy space $h^1_w$ if and only if this operator is uniformly bounded on all $h^1_w$-atoms. As an application, we show that every pseudo-differential operator of order zero has a bounded extension to $h^1_w$.
