Geodesic
Hardy spaces $H^1$ for Schrödinger operators with certain potentials
Jacek Dziubański1 ; Jacek Zienkiewicz1
1Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland
Studia Mathematica, Tome 164 (2004) no. 1, pp. 39-53
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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 $H^1_L$.
DOI : 10.4064/sm164-1-3
Keywords: semigroup linear operators generated schr dinger operator l mit delta v geq say belongs mathop sup infty state conditions which allow atomic characterization space

Jacek Dziubański  1   ; Jacek Zienkiewicz  1

1 Institute of Mathematics University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland 
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 for {Schr\"odinger} operators with certain potentials},
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Jacek Dziubański; Jacek Zienkiewicz. Hardy spaces $H^1$
 for Schrödinger operators with certain potentials. Studia Mathematica, Tome 164 (2004) no. 1, pp. 39-53. doi: 10.4064/sm164-1-3

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