## Journal of the Mathematical Society of Japan

### Classes of weights and second order Riesz transforms associated to Schrödinger operators

Fu Ken LY

#### 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.

#### Article information

Source
J. Math. Soc. Japan, Volume 68, Number 2 (2016), 489-533.

Dates
First available in Project Euclid: 15 April 2016

https://projecteuclid.org/euclid.jmsj/1460727369

Digital Object Identifier
doi:10.2969/jmsj/06820489

Mathematical Reviews number (MathSciNet)
MR3488134

Zentralblatt MATH identifier
1348.35060

#### Citation

LY, Fu Ken. Classes of weights and second order Riesz transforms associated to Schrödinger operators. J. Math. Soc. Japan 68 (2016), no. 2, 489--533. doi:10.2969/jmsj/06820489. https://projecteuclid.org/euclid.jmsj/1460727369

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