论文标题
边界弱 - 型稀疏双线性形式的估计，涉及$ a_ \ infty $最大功能
Borderline Weak--Type Estimates for Sparse Bilinear Forms Involving $A_\infty$ Maximal Functions
论文作者
论文摘要
对于任何可以通过稀疏双线性形式主导的操作员$ t $，我们证明$ t $是从$ l^1（\ widetilde {m} w）$限制为弱的 - $ l^1（w）$。我们的主要创新是$ \ widetilde {m} $是直接使用本地$ a_ \ infty $特征（而不是orlicz norms）来定义的最大函数。先前的结果归功于Coifman \＆Fefferman，Pérez，Hytönen\＆Pérez和Domingo-Salazar \＆Lacey \＆Rey。正如我们讨论的那样，但没有证明，我们使用的最大函数似乎按$ m_ {l（{log log} l）（{log log log log} l）（{log log log log log log} l）^{1+ε}} $。
For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^1(\widetilde{M}w)$ into weak--$L^1(w)$. Our main innovation is that $\widetilde{M}$ is a maximal function defined by directly using the local $A_\infty$ characteristic of the weight (rather than Orlicz norms). Prior results are due to Coifman\&Fefferman, Pérez, Hytönen\&Pérez, and Domingo-Salazar\&Lacey\&Rey. As we discuss, but do not prove, the maximal functions we use seem to be on the order of $M_{L({log log} L) ({log log log} L) ({log log log log} L)^{1+ε}}$.
