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April, 2016 Classes of weights and second order Riesz transforms associated to Schrödinger operators
Fu Ken LY
J. Math. Soc. Japan 68(2): 489-533 (April, 2016). DOI: 10.2969/jmsj/06820489

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.

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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

Information

Published: April, 2016
First available in Project Euclid: 15 April 2016

zbMATH: 1348.35060
MathSciNet: MR3488134
Digital Object Identifier: 10.2969/jmsj/06820489

Subjects:
Primary: 35J10, 42B20
Secondary: 42B35

Rights: Copyright © 2016 Mathematical Society of Japan

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Vol.68 • No. 2 • April, 2016
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