On the failure of lower square function estimates in the non-homogeneous weighted setting
On the failure of lower square function estimates in the non-homogeneous weighted setting
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关于非齐次加权设置中下平方函数估计的失败
DOI：
10.1007/s00208-018-1787-4
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发表时间：
2017
影响因子：
1.4
通讯作者：
A. Volberg
中科院分区：
文献类型：
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作者：
K. Domelevo;P. Ivanisvili;S. Petermichl;S. Treil;A. Volberg
我们证明了经典的A_{\infty } A∞条件对于非齐次加权L^2L2空间中的下平方函数估计是不充分的.我们还表明，在鞅$$A_2 $$A2条件下，估计成立，但即使考虑经典$$A_2 $$A2特征，该特征的最佳幂也从1 / 2跳到1。这是在一个鲜明的对比，以已知的估计在二进齐次设置以及最近的积极成果，在这个方向上的离散时间非齐次鞅变换。最后，我们给出了n阶齐次情形下随n增长的A_{\infty } A∞估计。
We show that the classical $$A_{\infty }$$A∞ condition is not sufficient for a lower square function estimate in the non-homogeneous weighted $$L^2$$L2 space. We also show that under the martingale $$A_2$$A2 condition, an estimate holds true, but the optimal power of the characteristic jumps from 1 / 2 to 1 even when considering the classical $$A_2$$A2 characteristic. This is in a sharp contrast to known estimates in the dyadic homogeneous setting as well as the recent positive results in this direction on the discrete time non-homogeneous martingale transforms. Last, we give a sharp $$A_{\infty }$$A∞ estimate for the n-adic homogeneous case, growing with n.