一个限制弱型不等式及其对Tp定理和CZO最优消去条件的应用
A restricted weak type inequality with application to a Tp theorem and optimal cancellation conditions for CZO's
摘要：
本文继续在arXiv：1906.05602中开始的研究，将David和Journé的T1定理和最优抵消条件扩展到更一般的权重对。这里主要的附加工具是两个重量限制弱型不等式。设σ和ω是局部有限的正Borel测度，其中一个为A无穷权，证明了α-分数次Calderón-Zygmund奇异积分T的两权限制弱型不等式成立当且仅当经典的分数次Muckenhoupt条件成立.在α = 0的情形下，T在未加权L2上也是有界的.应用程序，然后给出了一个TP定理的CZO的权重加倍时，一个是A无穷大，然后到最佳取消条件的CZO的多项式测试在类似的情况下。
英文摘要：
This paper continues the investigation begun in arXiv:1906.05602 of extending the T1 theorem of David and Journé, and optimal cancellation conditions, to more general weight pairs. The main additional tool developed here is a two weight restricted weak type inequality. Assuming σ and ω are locally finite positive Borel measures, with one of them an A infinity weight, we show that the two weight restricted weak type inequality for an α-fractional Calderón-Zygmund singular integral T holds if and (provided T is elliptic) only if the classical fractional Muckenhoupt condition holds. In the case α = 0, boundedness of T on unweighted L2 is assumed as well. Applications are then given to a Tp theorem for CZO's with doubling weights when one is A infinity, and then to optimal cancellation conditions for CZO's in terms of polynomial testing in similar situations.
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