Hardy spaces $H^1$ for Schrödinger operators with certain potentials
Volume 164 / 2004
Studia Mathematica 164 (2004), 39-53
MSC: Primary 42B30, 42B25, 35J10; Secondary 47D03.
DOI: 10.4064/sm164-1-3
Abstract
Let $\{ K_t\} _{t>0}$ be the semigroup of linear operators generated by a Schrödinger operator $-L={\mit \Delta } -V$ with $V\geq 0$. We say that $f$ belongs to $H_L^1$ if $\| \mathop {\rm sup}_{t>0}|K_tf(x)|\, \| _{L^1(dx)}<\infty $. We state conditions on $V$ and $K_t$ which allow us to give an atomic characterization of the space $H^1_L$.
