论文标题
$ l^2 $ blandentialcalderón-Zygmund运营商
The $L^2$-boundedness of the variational Calderón-Zygmund operators
论文作者
论文摘要
在本文中，我们验证了Calderón-Zygmund的跳跃功能和变化的$ l^2 $结合度，以及满足基础核的\ begin {align*} \ int _ {\ int _ {\ varepsilon \ varepsilon \ leq leq leq x-y | x-y | \ leq | \ e | \ leq | \ leq | \ e | \ leq | \ e | k（x，y）dy = \ int _ {\ varepsilon \ leq | x-y | \ leq n} k（x，y）dx = 0 \; \ forall 0 <\ varepsilon \ leq n <\ infty，\ end {align*}除了某些适当的尺寸和光滑的条件外。该结果应该是内核变异不平等的第一个一般标准，不一定是卷积类型。我们在这里验证的$ l^2 $结合度的假设也是（急剧加权规范不平等现象）的相关结果的起点，出现在许多最近的论文中。
In this paper, we verify the $L^2$-boundedness for the jump functions and variations of Calderón-Zygmund singular integral operators with the underlying kernels satisfying \begin{align*}\int_{\varepsilon\leq |x-y|\leq N} K(x,y)dy=\int_{\varepsilon\leq |x-y|\leq N}K(x,y)dx=0\; \forall 0<\varepsilon\leq N<\infty,\end{align*} in addition to some proper size and smooth conditions. This result should be the first general criteria for the variational inequalities for kernels not necessarily of convolution type. The $L^2$-boundedness assumption that we verified here is also the starting point of the related results on the (sharp) weighted norm inequalities appeared in many recent papers.
