发表机构
University of Würzburg（维尔茨堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明了二维整数格上离散Beurling--Ahlfors算子虚部的sharp $\ell^p$ 范数界为 $p^\star-1$，通过鞅表示但需克服强微分从属缺失的困难。
AI 中文摘要
我们证明了在 $\mathbb{Z}^2$ 上离散Beurling--Ahlfors算子虚部的sharp $\ell^p$ 界为 $p^\star-1$。该算子通过复合泊松跳跃过程和热延拓允许一个鞅表示，但附属于函数的鞅与其变换的鞅不满足强微分从属关系，因此算子范数估计无法通过先前的工作获得。
英文摘要
We prove the sharp $\ell^p$ bound $p^\star-1$ for certain second-order discrete Riesz transforms on products of integers, in all dimensions. The family includes the imaginary part of the discrete Beurling-Ahlfors operator in dimension two as a special case. While these operators admit a martingale representation via compound Poisson jump processes and heat extensions, the martingale attached to a function and the martingale attached to its transform do not enjoy strong differential subordination, so the operator-norm estimate is not accessible through prior work.
Comments20 pages. Added extension of the result to all dimensions. Corrected typos and added references
