论文标题
在沿二次超曲面的多项式Carleson操作员上
On Polynomial Carleson operators along quadratic hypersurfaces
论文作者
论文摘要
我们证明，由$（y，q（y））\ subseteq \ mathbb {r}^{n+1} $定义的最大调制的奇异振荡性积分算子，用于任意非分数Quadratic form $ q $，以$ 1 $ n $ 1 $ n $ 1 $ <P < 2 $。该操作员采用ra型多项式的Carleson操作员的形式，其中最大调制阶段位于$ \ {p_2，\ ldots，p_d \} $的真实跨度，对于任何固定的真实价值p_j $ p_j $，$ j $ y y $ j $ y y y y y y y y y y y y y y $ j $ $ q（y）$。这项工作中开发的一般方法适用于任意签名的二次形式，而先前的工作仅考虑了特殊的正定情况$ q（y）= | y |^2 $。
We prove that a maximally modulated singular oscillatory integral operator along a hypersurface defined by $(y,Q(y))\subseteq \mathbb{R}^{n+1}$, for an arbitrary non-degenerate quadratic form $Q$, admits an a priori bound on $L^p$ for all $1<p<\infty$, for each $n \geq 2$. This operator takes the form of a polynomial Carleson operator of Radon-type, in which the maximally modulated phases lie in the real span of $\{p_2,\ldots,p_d\}$ for any set of fixed real-valued polynomials $p_j$ such that $p_j$ is homogeneous of degree $j$, and $p_2$ is not a multiple of $Q(y)$. The general method developed in this work applies to quadratic forms of arbitrary signature, while previous work considered only the special positive definite case $Q(y)=|y|^2$.
