论文标题
$ l^p $估算的希尔伯特变换和最大运算符与可变多项式关联
$L^p$ estimates for Hilbert transform and maximal operator associated to variable polynomial
论文作者
论文摘要
我们沿一类可变的非灯多项式曲线$（p（t），u（x）t）$沿着可测量的$ u（x）$进行了调查的希尔伯特变换和最大运算符，并证明$ 1 <p <p <\ infty $。特别是，通过变量更改，这些均匀估计值等于曲线$（p（v（x）t），t）$的曲线估计值，其可测量$ V（x）$。为了获得所需的界限，我们充分利用时频技术，并为某些特殊单独的设置建立至关重要的$ε$提示估算。
We investigate the Hilbert transform and the maximal operator along a class of variable non-flat polynomial curves $(P(t),u(x)t)$ with measurable $u(x)$, and prove uniform $L^p$ estimates for $1<p<\infty$. In particular, via the change of variable, these uniform estimates are equal to the ones for the curves $(P(v(x)t),t)$ with measurable $v(x)$. To obtain the desired bound, we make full use of time-frequency techniques and establish a crucial $ε$-improving estimate for some special separate sets.
