Abstract
We consider the Schrödinger operator $-\Delta+V$ on $\mathbb{R}^{n}$ with $n\ge 3$ and $V$ a member of the reverse Hölder class $\mathcal{B}_s$ for some $s$ > $n/2$. We obtain the boundedness of the second order Riesz transform $\nabla^2 (-\Delta+V)^{-1}$ on the weighted spaces $L^p(w)$ where $w$ belongs to a class of weights related to $V$. To prove this, we develop a good-$\lambda$ inequality adapted to this setting along with some new heat kernel estimates.
Citation
Fu Ken LY. "Classes of weights and second order Riesz transforms associated to Schrödinger operators." J. Math. Soc. Japan 68 (2) 489 - 533, April, 2016. https://doi.org/10.2969/jmsj/06820489
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