论文标题
calder $ \ acute {\ rm o} $ n-zygmund类型单数积分的扩展
An Extension of Calder$\acute{\rm O}$n-Zygmund type singular integral
论文作者
论文摘要
在本文中，我们认为一种单数积分可以被视为经典calder $ \ acute {\ rm o} $ n-zygmund型单数积分的扩展。我们以$ 1 <q <\ infty $的价格建立了$ l^q $空间中单数积分的估计。特别是，可以从我们获得的估算中恢复calder $ \ actute {\ rm o} $ n-zygmund估算。我们主要结果的证明是通过所谓的“几何方法”的证明，该方法在\ cite {cp}中应用于椭圆方程的$ l^q $估计值，以及\ cite {lw，wang}在calder $ \ acter $ \ acte {lw，wang，wang，wang}上。
In this paper, we consider a kind of singular integral which can be viewed as an extension of the classical Calder$\acute{\rm o}$n-Zygmund type singular integral. We establish an estimate of the singular integral in the $L^q$ space for $1<q<\infty$. In particular, the Calder$\acute{\rm o}$n-Zygmund estimate can be recovered from our obtained estimate. The proof of our main result is via the so called "geometric approach", which was applied in \cite{CP} on the $L^q$ estimate of the elliptic equations and in \cite{LW,Wang} on a new proof of the the Calder$\acute{\rm o}$n-Zygmund estimate.
