论文标题
三线性平滑不平等和三角形希尔伯特变换的变体
Trilinear smoothing inequalities and a variant of the triangular Hilbert transform
论文作者
论文摘要
勒布斯格空间不等式证明了涉及曲率的三角形希尔伯特变换的变体。该分析依赖于本文中产生的至关重要的三线性平滑不平等，以及扭曲副膜的各向异性变体的边界。三线性平滑不等式还导致相应的最大函数和定量非线性Roth型定理的Lebesgue空间边界，涉及欧几里得平面中的模式。
Lebesgue space inequalities are proved for a variant of the triangular Hilbert transform involving curvature. The analysis relies on a crucial trilinear smoothing inequality developed herein, and on bounds for an anisotropic variant of the twisted paraproduct. The trilinear smoothing inequality also leads to Lebesgue space bounds for a corresponding maximal function and a quantitative nonlinear Roth-type theorem concerning patterns in the Euclidean plane.
