论文标题
基质重量的外推和分解
Extrapolation and Factorization of matrix weights
论文作者
论文摘要
在本文中，我们证明了琼斯分解定理和矩阵$ \ mathcal a_p $ striges的卢比奥·德·弗朗西亚推断定理。这些结果回答了矩阵权重的研究中长期存在的开放问题。该证明需要发展凸面有价值函数和可测量的eminorm函数的理论。特别是，我们定义了Hardy Littlewood Maxal Operator的凸面有价值的版本，并构建了Rubio de Francia Iteration算法的适当概括，这是标量案例中两种结果的核心。
In this paper we prove the Jones factorization theorem and the Rubio de Francia extrapolation theorem for matrix $\mathcal A_p$ weights. These results answer longstanding open questions in the study of matrix weights. The proof requires the development of the theory of convex-set valued functions and measurable seminorm functions. In particular, we define a convex-set valued version of the Hardy Littlewood maximal operator and construct an appropriate generalization of the Rubio de Francia iteration algorithm, which is central to the proof of both results in the scalar case.
