退化抛物型Riesz变换在粗糙系数下的有界性结果
A boundedness result for degenerate parabolic Riesz transforms with rough coefficients
- Université Paris-Saclay（巴黎萨克雷大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文证明退化抛物型Riesz变换在$p \le 2$范围内的有界性，利用非对角估计与加权嵌入，获得由权函数逆Hölder类量化的指数范围，实系数时精确至$1$。
AI中文摘要：
本文证明了与退化抛物型算子相关的抛物型Riesz变换在$p \le 2$范围内的有界性结果，其中该算子的椭圆部分为散度形式，系数为依赖于空间和时间的可测复值函数。退化性由Muckenhoupt类$A_2(\mathbb{R}^n)$中的空间权函数决定。论证依赖于预解族抛物梯度的非对角估计以及加权嵌入。我们在严格低于$2$的指数范围内获得了有界性，其具体范围由权函数的逆Hölder类量化。对于实系数情形，该量化是精确的，并可延拓至$1$。
英文摘要：
In this paper, we prove a boundedness result for parabolic Riesz transforms in the range $p \le 2$ associated with degenerate parabolic operators whose elliptic part is in divergence form with complex coefficients depending measurably on space and time. The degeneracy is determined by a spatial weight in the Muckenhoupt class $A_2(\mathbb{R}^n)$. The argument relies on off-diagonal estimates for the parabolic gradient of the resolvent family, together with weighted embeddings. We obtain boundedness in a range of exponents strictly below $2$, with explicit ranges quantified by the reverse Hölder class of the weight. For real coefficients, this quantification is sharp and extends down to $1$.
