论文标题
与傅立叶乘数和应用相关的最大运算符
Maximal operators associated with Fourier multipliers and applications
论文作者
论文摘要
在本文中，我们介绍了一个与傅立叶乘数相关的最大运算符的标准，该标准将在$ l^p（\ mathbb {r}^d）$上限制。满足标准的值得注意的例子是Mikhlin类型的乘数或有限的衰减，不一定是径向。为此，我们利用修改的平方功能估计和双线性插值。因此，我们获得了分数半波方程和表面平均值以及最大运算符的$ l^p $界限的收敛结果。
In this paper, we introduce a criterion for maximal operators associated with Fourier multipliers to be bounded on $L^p(\mathbb{R}^d)$. Noteworthy examples satisfying the criterion are multipliers of the Mikhlin type or limited decay which are not necessarily radial. To do so, we make use of modified square function estimates and bilinear interpolation. In result, we obtain convergence results for fractional half-wave equations and surface averages as well as the $L^p$ boundedness for the maximal operators.
