Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces
Weak type estimates and Cotlar inequalities for Calderón-Zygmund operators on nonhomogeneous spaces
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DOI：
10.1155/s1073792898000312
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发表时间：
1997-11
影响因子：
1
通讯作者：
F. Nazarov;S. Treil;A. Volberg
中科院分区：
文献类型：
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作者：
F. Nazarov;S. Treil;A. Volberg
经典的Calderon-Zygmund算子理论是从研究奇异核实线上的卷积算子开始的。(这种算子的一个典型例子是所谓的希尔伯特变换，定义为Hf（t) =∫R f(s) ds t−s。）后来它发展成为一个很大的分析分支，涵盖了抽象测度空间（所谓的“齐次型空间”）上相当广泛的一类奇异积分算子。为了了解这一理论在过去30年里发展了多远，将斯坦于1970年出版的经典教科书[St1]与[DJ]、[St2]、[Ch2]和[CW]中的现代理论大纲进行比较就足够了。[St1]仍然是对这一主题的优秀介绍。直到最近，唯一没有受到挑战的是该测量的倍性，即假设对于某个常数C >0，
The classical theory of Calderon–Zygmund operators started with the study of convolution operators on the real line having singular kernels. (A typical example of such an operator is the so called Hilbert transform, defined by Hf(t) = ∫ R f(s) ds t−s .) Later it has developed into a large branch of analysis covering a quite wide class of singular integral operators on abstract measure spaces (so called “spaces of homogeneous type”). To see how far the theory has evolved during the last 30 years, it is enough to compare the classical textbook [St1] by Stein published in 1970 (which remains an excellent introduction to the subject) to the modern outline of the theory in [DJ], [St2], [Ch2], and [CW]. The only thing that has remained unchallenged until very recently was the doubling property of the measure, i.e., the assumption that for some constant C > 0,