Journal of the Mathematical Society of Japan

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

Fu Ken LY

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1460727369

Digital Object Identifier
doi:10.2969/jmsj/06820489

Mathematical Reviews number (MathSciNet)
MR3488134

Zentralblatt MATH identifier
1348.35060

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx] 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B35: Function spaces arising in harmonic analysis

Keywords
weights Schrödinger operators good-$\lambda$ inequalities Riesz transforms heat kernels reverse Hölder

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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