L^p中奇异积分的伪局部化
Pseudo-localisation of singular integrals in L^p
摘要：
作为发展非对易Calderon-Zygmund理论的一步，J. Parcet（J. Funct.肛门，2009）建立了经典奇异积分的一个新的伪局部化原理，证明了Tf在一个只依赖于L^2中的f而不依赖于任意规范化的Calderon-Zygmund算子T的集合之外具有小的L^2范数. Parcet还问，对于1 < p < infinity，类似的结果是否在L^p中成立。本文对此作了肯定的回答。基于鞅技巧的证明，甚至在原来的L^2结果上有所改进。
英文摘要：
As a step in developing a non-commutative Calderon-Zygmund theory, J. Parcet (J. Funct. Anal., 2009) established a new pseudo-localisation principle for classical singular integrals, showing that Tf has small L^2 norm outside a set which only depends on f in L^2 but not on the arbitrary normalised Calderon-Zygmund operator T. Parcet also asked if a similar result holds true in L^p for 1 < p < infinity. This is answered in the affirmative in the present paper. The proof, which is based on martingale techniques, even somewhat improves on the original L^2 result.
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