论文标题
截短的单数ra算子的振荡估计值
Oscillation estimates for truncated singular Radon operators
论文作者
论文摘要
在本文中，我们证明了对$ l^p $的统一振荡估计，其中$ p \ in（1，\ infty）$，用于与Calderón-Zygmund内核相关的截短的rad型截断，均连续和离散设置。在离散的情况下，我们使用Ionescu-Wainger乘数定理和Rademacher-Menshov不平等，以处理离散奇异积分的数量理论性质。我们在连续设置中获得的结果可以看作是Calderón-Zygmund类型的连续奇异积分的坎贝尔，琼斯，莱因霍尔德和Wierdl结果的概括。
In this paper we prove uniform oscillation estimates on $L^p$, with $p\in(1,\infty)$, for truncated singular integrals of the Radon type associated with Calderón-Zygmund kernel, both in continuous and discrete settings. In the discrete case we use the Ionescu-Wainger multiplier theorem and the Rademacher-Menshov inequality to handle the number-theoretic nature of the discrete singular integral. The result we obtained in the continuous setting can be seen as a generalisation of the results of Campbell, Jones, Reinhold and Wierdl for the continuous singular integrals of the Calderón-Zygmund type.
