论文标题
加权理论的必要条件
Necessary/sufficient conditions in weighted theory
论文作者
论文摘要
我们在加权理论中基本和基本条件之间提供了一个完全完整的词典，例如加倍，一个权重A_P（W），A__ \ INFTY和C_P条件以及两个权重A_P以及“缓冲液”能量和关键条件。最值得注意的含义是，在A_ \ Infty权重的情况下，两个权重A_P条件意味着P-Pivotal条件，因此，就现有T1理论而言，p = 2的已知NTV转换的优雅和简短证明了p = 2。我们还提供了一个非常技术性的构建，灵感来自[6]，证明我们可以使不在A_ \ Infty中的C_P条件的重量增加一倍。
We provide an essentially complete dictionary of all implications among the basic and fundamental conditions in weighted theory such as the doubling, one weight A_p(w), A_\infty and C_p conditions as well as the two weight A_p and the "buffer" Energy and Pivotal conditions. The most notable implication is that in the case of A_\infty weights the two weight A_p condition implies the p-Pivotal condition hence giving an elegant and short proof of the known NTV-conjecture with p=2 for A_\infty weights in terms of existing T1 theory. We also provide a quite technical construction inspired by [6] proving that we can have doubling weights satisfying the C_p condition which are not in A_\infty.
