BMO for nondoubling measures
BMO for nondoubling measures
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DOI：
10.1215/s0012-7094-00-10238-4
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发表时间：
2000-05
影响因子：
2.5
通讯作者：
J. Mateu;P. Mattila;A. Nicolau;J. Orobitg
中科院分区：
文献类型：
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作者：
J. Mateu;P. Mattila;A. Nicolau;J. Orobitg
1.导论.奇异积分的Calderón-Zygmund理论传统上被认为是关于满足加倍条件的测度。最近，Tolsa [T]和Nazarov，Treil和Volberg [NTV]独立地证明了这种标准的加倍条件并不是真正必要的。同样，在齐次空间中，有界平均振荡函数BMO及其前对偶H1原子哈代空间在奇异积分理论中也起着重要作用.本文试图在基本测度为非倍测度时，为空间BMO和H1寻找好的替代.我们的希望是，我们将能够证明一些结果的托尔萨，纳扎罗夫，特雷尔，和沃尔伯格，通过BMO-H 1插值，但在这方面，我们是不成功的。设μ是Rn上的非负Radon测度。一个函数f ∈ L 1 loc（μ）被称为属于BMO（μ），如果不等式
1. Introduction. The Calderón-Zygmund theory of singular integrals has been traditionally considered with respect to a measure satisfying a doubling condition. Recently, Tolsa [T] and, independently, Nazarov, Treil, and Volberg [NTV] have shown that this standard doubling condition was not really necessary. Likewise, in the homogeneous spaces setting, functions of bounded mean oscillation, BMO, and its predual H 1 , the atomic Hardy space, play an important role in the theory of singular integrals. This note is an attempt to find good substitutes for the spaces BMO and H 1 when the underlying measure is nondoubling. Our hope was that we would have been able to prove some results of Tolsa, Nazarov, Treil, and Volberg, via BMO-H 1 interpolation, but in this respect we were unsuccessful. Let µ be a nonnegative Radon measure on R n. A function f ∈ L 1 loc (µ) is said to belong to BMO(µ) if the inequality