A Weighted Estimate For The Commutator Kakeya Maximal Operator On Functions Of Product Type

From the literature we have known, Kakeya conjecture and Kakeya maximal function conjecture have some close relations. Kakeya maximal function conjecture implies Kakeya conjecture. There have many estimates about Kakeya conjecture. One has attempted to solve Kakeya conjecture from Kakeya maximal function by using different methods. This paper posed an estimate of commutator Kakeya maximal function.In this paper, we have proven a weighted commutator Kakeya maximal function estimate on function of product type.The paper is divided into two chapters. In chapter one, we simply introducted what the predecessor had done about Kakeya maximal function. We also introduced reverse Ho|¨lder weighted function and BMO as preparation knowledge.In the second chapter, the detailed proof of the main result has given, we divided Kakeya commutator maximal function into three parts, then estimated one by one. Meanwhile, we have pointed out the limitation of the method. We hoped that we can discover a better method and obtain a better result, and hoped our result can do something to understand Kakeya conjecture and Kakeya maximal function conjecture.