带常数漂移的Riesz变换的无维弱(1,1)估计
Dimension-free weak $(1,1)$ estimates for Riesz transforms with constant drift
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中文总结 AI 辅助
本文证明带常数漂移的Riesz变换满足常数至多2的弱(1,1)估计，且一致于维数和漂移，并推广分数障碍方法至指数加权情形，进而得到强L^p界。
中文摘要 AI 辅助
设$L_v=-\Delta-2v\cdot\nabla$作用于$L^2(\mathbb R^n,e^{2v\cdot x},dx)$，其中$v\in\mathbb R^n\setminus\{0\}$为常数漂移向量。我们证明，对于实值函数，全向量Riesz变换$\nabla L_v^{-1/2}$满足弱型$(1,1)$估计，常数至多为$2$，且该常数关于维数和漂移向量一致。我们的证明将Ouyang、Spector和Stockdale（https://arxiv.org/abs/2608.18068）的分数障碍方法推广到指数加权情形。插值随后给出$1<p\le 2$时的强$L^p$界，常数仅依赖于$p$。
英文摘要
Let $L_v=-Δ-2v\cdot\nabla$ on $L^2(\mathbb R^n,e^{2v\cdot x}\,dx)$, where $v\in\mathbb R^n\setminus\{0\}$ is a constant drift vector. We prove that the full vector Riesz transform $\nabla L_v^{-1/2}$ satisfies a weak-type $(1,1)$ estimate for real-valued functions with constant at most $2$, uniformly in both the dimension and the drift vector. Our proof extends the fractional obstacle method of Ouyang, Spector and Stockdale (https://arxiv.org/abs/2608.18068) to the exponentially weighted setting. Interpolation then yields strong $L^p$ bounds for $1<p\le 2$, with constants depending only on $p$.
发表机构
- Indian Institute of Technology Bombay（印度理工学院孟买分校）
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