Abstract In this paper, we consider a kind of singular integral which can be viewed as an extension of the classical Calderon-Zygmund type singular integral. We establish an estimate of the singular integral in the L q space for 1 q ∞ . In particular, the Calderon-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 [1] on the L q estimate of the elliptic equations and in [4] , [6] on a new proof of the the Calderon-Zygmund estimate.

中文翻译：

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Calderón-Zygmund 型奇异积分的扩展

摘要 在本文中，我们考虑一种奇异积分，它可以看作是经典Calderon-Zygmund 型奇异积分的扩展。我们建立了 L q 空间中 1 q ∞ 奇异积分的估计。特别是，可以从我们获得的估计中恢复 Calderon-Zygmund 估计。我们主要结果的证明是通过所谓的“几何方法”进行的，该方法在[1]中应用于椭圆方程的 L q 估计，在 [4]、[6] 中应用于 Calderon-齐格蒙德估计。