带负位势的薛定谔算子的里斯变换
Riesz transforms associated to Schrödinger operators with negative potentials
摘要：
本文研究了势$V$在不同条件下的里斯变换$\na A^{-1/2}$，其中$A$是薛定谔算子$-\D-V, V\ge 0$.证明了如果$V$是强次临界的，则对所有的$p\in(p_0';2]$，$\na A^{-1/2}$在$L^p(\R^N)$，$N\ge3$上有界，其中$p_0'$是$p_0$的对偶指数，$2< \frac{2N}{N-2}
英文摘要：
The goal of this paper is to study the Riesz transforms $\na A^{-1/2}$ where $A$ is the Schrödinger operator $-\D-V, V\ge 0$, under different conditions on the potential $V$. We prove that if $V$ is strongly subcritical, $\na A^{-1/2}$ is bounded on $L^p(\R^N)$, $N\ge3$, for all $p\in(p_0';2]$ where $p_0'$ is the dual exponent of $p_0$ where $2<\frac{2N}{N-2}
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