A spectral multiplier theorem for $H\sp 1$ spaces associated with Schrödinger operators with potentials satisfying a reverse Hölder inequality
Dziubański, Jacek
Illinois J. Math., Tome 45 (2001) no. 4, p. 1301-1313 / Harvested from Project Euclid
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Let $\{ T_t\}_{t>0}$ be the semigroup of linear operators generated by a Schrödinger operator $-A=\Delta -V$ on $\mathbb{R}^d$, where $V$ is a nonnegative nonzero potential satisfying a reverse Hölder inequality, and let $\int_0^\infty \lambda \, dE_A(\lambda )$ be the spectral resolution of $A$. We say that a function $f$ is an element of $H_A^1$ if the maximal function $\mathcal{M}f(x)=\sup_{t>0} |T_tf(x)|$ belongs to $L^1$. We prove that if a function $F$ satisfies a Mihlin condition with exponent $\alpha >d/2$ then the operator $F(A)=\int_0^\infty F(\lambda )\, dE_A(\lambda )$ is bounded on $H_A^1$.
Publié le : 2001-10-15
Classification:  35J10,  35P05,  42B20,  47D08,  47F05 
@article{1258138067,
     author = {Dziuba\'nski, Jacek},
     title = {A spectral multiplier theorem for $H\sp 1$ spaces associated with Schr\"odinger operators with potentials satisfying a reverse H\"older inequality},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 1301-1313},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138067}
}

Dziubański, Jacek. A spectral multiplier theorem for $H\sp 1$ spaces associated with Schrödinger operators with potentials satisfying a reverse Hölder inequality. Illinois J. Math., Tome 45 (2001) no. 4, pp.  1301-1313. http://gdmltest.u-ga.fr/item/1258138067/