标题： 双线性粗糙奇异积分的另一种方法 显示英文标题

标题： An alternate approach to bilinear rough singular integrals

摘要： 本文的目标是提供一种新方法来解决双线性粗糙奇异积分算子的$L^p-$有界性问题。该方法依赖于输入函数的局部傅里叶级数展开，从而得到在频率参数上具有期望衰减的三线性估计。这种方法不同于 Grafakos、He 和 Honzík 在其工作中以及随后一系列关于双线性粗糙奇异积分论文中所采用的乘子的小波分解方法。通过这种方法，我们提供了双线性粗糙奇异积分算子在维度一的情况下，在最优指数范围内的$L^p-$有界性的新的和自包含的证明。此外，这种方法使我们能够在核在平面上远离对角线时，证明极大截断的双线性粗糙奇异积分的尖锐$L^p-$估计。 显示英文摘要

摘要： The goal of this paper is to provide a new approach to address the $L^p-$boundedness of bilinear rough singular integral operators. This approach relies on local Fourier series expansion of input functions leading to trilinear estimates with desired decay in the frequency parameter. This approach departs from the existing methods of the wavelet decomposition of the multiplier employed in the work of Grafakos, He and Honz\'ik and in a series of subsequent papers in the context of bilinear rough singular integrals. With this new approach, we provide a new and self contained proof of $L^p-$boundedness of bilinear rough singular integral operators in dimension one for the optimal range of exponents. Furthermore, this approach allows us to prove sharp $L^p-$estimates for maximally truncated bilinear rough singular integrals when the kernel is supported away from the diagonal in the plane.