论文标题
方向平方函数
Directional square functions
论文作者
论文摘要
Fefferman对球乘数的反例的定量公式与锥形和方向乘数的平方函数估计自然相关。在本文中，我们基于Carleson序列的定理和多参数时频分析技术开发了这些平方函数估计的新框架。作为应用程序，我们证明了圆锥形乘数的Rubio de Francia型平方函数和乘数适用于指向沿$ n $方向的矩形的锐利型方形功能的尖锐或量化的边界。这些估计值的合适组合产生了一个新的，目前最著名的对数，以傅立叶限制为$ n $ gon，从而改善了A. Cordoba的先前结果。我们的方向性Carleson嵌入扩展到加权设置，得出了先前未知的加权估计值，用于定向最大功能和奇异积分。
Quantitative formulations of Fefferman's counterexample for the ball multiplier are naturally linked to square function estimates for conical and directional multipliers. In this article we develop a novel framework for these square function estimates, based on a directional embedding theorem for Carleson sequences and multi-parameter time-frequency analysis techniques. As applications we prove sharp or quantified bounds for Rubio de Francia type square functions of conical multipliers and of multipliers adapted to rectangles pointing along $N$ directions. A suitable combination of these estimates yields a new and currently best-known logarithmic bound for the Fourier restriction to an $N$-gon, improving on previous results of A. Cordoba. Our directional Carleson embedding extends to the weighted setting, yielding previously unknown weighted estimates for directional maximal functions and singular integrals.
