论文标题
$ c_ {w^*}^{1，α} $常规曲线的单数积分
Singular integrals on $C_{w^*}^{1,α}$ regular curves in Banach duals
论文作者
论文摘要
现代对飞机曲线上奇异整体操作员的现代研究始于1970年代。从那时起，就在欧几里得空间中较低维集的奇异积分运算符的界面上进行了大量工作。近年来，数学家试图将这些结果推向更通用的度量设置，尤其是在Carnot组的曲线和图形上定义的单数积分运算符的情况下。 假设$ x = y^*$对于可分开的Banach Space $ Y $。任何可分开的度量空间都可以通过kuratowski嵌入在这种Banach空间中嵌入。 Suppose $Γ= γ([a,b])$ is a curve in $X$ whose $w^*$-derivative is Hölder continuous and bounded away from 0. We prove that any convolution type singular integral operator associated with a 1-dimensional Calderón-Zygmund kernel which is uniformly $L^2$-bounded on lines is $L^p$-bounded along $Γ$. 我们还证明了David的``好Lambda''定理的版本，用于两倍的度量空间上的常规措施。
The modern study of singular integral operators on curves in the plane began in the 1970's. Since then, there has been a vast array of work done on the boundedness of singular integral operators defined on lower dimensional sets in Euclidean spaces. In recent years, mathematicians have attempted to push these results into a more general metric setting particularly in the case of singular integral operators defined on curves and graphs in Carnot groups. Suppose $X = Y^*$ for a separable Banach space $Y$. Any separable metric space can be isometrically embedded in such a Banach space via the Kuratowski embedding. Suppose $Γ= γ([a,b])$ is a curve in $X$ whose $w^*$-derivative is Hölder continuous and bounded away from 0. We prove that any convolution type singular integral operator associated with a 1-dimensional Calderón-Zygmund kernel which is uniformly $L^2$-bounded on lines is $L^p$-bounded along $Γ$. We also prove a version of David's ``good lambda'' theorem for upper regular measures on doubling metric spaces.
