论文标题
可变各向异性奇异积分运算符
Variable Anisotropic Singular Integral Operators
论文作者
论文摘要
我们介绍了与连续的多级椭圆形封面相关的可变各向异性单数积分运算符的$ \ Mathbb {r}^n $，由Dahmen，Dekel和Petrushev \ cite {ddp}引入。这是在$ \ mathbb {r}^n $上的经典各向同性奇异积分运算符的扩展，并将其对第一作者\ cite {b}引入的一般膨胀矩阵的各向异性类似物及其各向异性类似物。我们在Hardy空间上建立了可变各向异性奇异积分运算符$ t $的界限，该空间具有尖锐的可变各向异性$ h^p（θ）$，由Dekel，Petrushev和Weissblat \ Cite \ Cite \ Cite {dpw}开发。与同质类型空间上强的空间的一般理论相反，我们的结果在整个范围内$ 0 <p \ leq 1 $。
We introduce the class of variable anisotropic singular integral operators associated to a continuous multi-level ellipsoid cover $Θ$ of $\mathbb{R}^n$ introduced by Dahmen, Dekel, and Petrushev \cite{ddp}. This is an extension of the classical isotropic singular integral operators on $\mathbb{R}^n$ of arbitrary smoothness and their anisotropic analogues for general expansive matrices introduced by the first author \cite{b}. We establish the boundedness of variable anisotropic singular integral operators $T$ on the Hardy spaces with pointwise variable anisotropy $H^p(Θ)$, which were developed by Dekel, Petrushev, and Weissblat \cite{dpw}. In contrast with the general theory of Hardy spaces on spaces of homogenous type, our results work in the full range $0<p\leq 1$.
