Journal of the Mathematical Society of Japan

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

Fu Ken LY

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

First available in Project Euclid: 15 April 2016

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Zentralblatt MATH identifier

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

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


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.

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