A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition
A proof of the weak (1,1) inequality for singular integrals with non doubling measures based on a Calderón-Zygmund decomposition
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DOI：
10.5565/publmat_45101_07
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发表时间：
2001
影响因子：
1.1
通讯作者：
X. Domènech
中科院分区：
文献类型：
--
作者：
X. Domènech
给定 ${\mathbb R}^d$ 上的加倍测度 $\mu$，调和分析的经典结果是，在 $L^2(\mu)$ 内有界的 Calderon-Zygmund 算子也是弱类型 (1,1)。最近的研究表明，如果用 $\mu$ 上的温和增长条件代替 $\mu$ 上的倍增条件，则同样的结果成立。本文给出了这一结果的另一个证明。该证明在精神上与加倍测度的经典论证非常接近，并且基于适应非加倍情况的新卡尔德隆-齐格蒙德分解。
Given a doubling measure $\mu$ on ${\mathbb R}^d$, it is a classical result of harmonic analysis that Calderon-Zygmund operators which are bounded in $L^2(\mu)$ are also of weak type (1,1). Recently it has been shown that the same result holds if one substitutes the doubling condition on $\mu$ by a mild growth condition on $\mu$. In this paper another proof of this result is given. The proof is very close in spirit to the classical argument for doubling measures and it is based on a new Calderon-Zygmund decomposition adapted to the non doubling situation.