Weighted martingale multipliers in non-homogeneous setting and outer measure spaces
Weighted martingale multipliers in non-homogeneous setting and outer measure spaces
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非均匀环境和外部测量空间中的加权鞅乘数
DOI：
10.1016/j.aim.2015.08.019
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
A. Volberg
中科院分区：
文献类型：
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作者：
Christoph Thiele;S. Treil;A. Volberg
研究了非齐次情况下，即参考测度ν不加倍时，加权空间l2 （w d ν）中鞅差的无条件基性质。具体地说，我们证明了量[w] a2 = sup I (< w>) I< w−1> I（通过相对于参考测度ν的平均值<⋅> I定义）的有限性，意味着Haar子空间在加权空间l2 （w d ν）中形成一个无条件基。此外，我们还证明了该系统的无条件基常数在[w] a2中最大为线性增长。这个问题被简化为所谓哈尔乘数的尖锐加权估计。即使在具有Lebesgue参考测度的R d中的标准并矢格的经典情况下，我们的结果也是新的，因为我们的估计与维数n无关。我们的方法结合了外测度空间技术和Bellman函数参数。
We investigate the unconditional basis property of martingale differences in weighted spaces L 2 (w d ν) in the non-homogeneous situation, that is when the reference measure ν is not doubling. Specifically, we prove that finiteness of the quantity [w] A 2= sup I< w> I< w− 1> I, defined through averages<⋅> I relative to the reference measure ν, implies that Haar subspaces form an unconditional basis in the weighted space L 2 (w d ν). Moreover, we prove that the unconditional basis constant of this system grows at most linearly in [w] A 2. The problem is reduced to the sharp weighted estimates of the so-called Haar multipliers. Even in the classical case of the standard dyadic lattice in R d with Lebesgue reference measure our result is new in that our estimates are independent of the dimension n. Our approach combines the technique of outer measure spaces with the Bellman function argument.
外测度的 Lp 理论与 Lennart Carleson 的两个主题相结合
DOI：
10.1090/s0273-0979-2014-01474-0
发表时间：
2015
期刊：
arXiv: Classical Analysis and ODEs
影响因子：
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作者：
C. Thiele
通讯作者：
C. Thiele