论文标题
一般的准巴纳赫功能空间中的外推
Extrapolation in general quasi-Banach function spaces
论文作者
论文摘要
在本文中，我们证明了非对抗，有限的范围，多线性，矢量值和两重版本的卢比奥·德弗朗西亚外推定定理在一般的准巴纳赫函数空间中。我们证明了将硬质木材最大运算符概括为非常通用的基础的映射属性，该基础包括一种方法来获得相对于其运营商规范的自我改进结果。此外，我们证明了在加权洛伦兹，可变的lebesgue和Morrey空间中的强硬木材最大运算符的界限，并在文献中恢复并扩展了几个推断定理。最后，我们将结果应用于Riesz电位和双线性希尔伯特变换。
In this paper we prove off-diagonal, limited range, multilinear, vector-valued, and two-weight versions of the Rubio de Francia extrapolation theorem in general quasi-Banach function spaces. We prove mapping properties of the generalization of the Hardy-Littlewood maximal operator to very general bases that includes a method to obtain self-improvement results that are sharp with respect to its operator norm. Furthermore, we prove bounds for the Hardy-Littlewood maximal operator in weighted Lorentz, variable Lebesgue, and Morrey spaces, and recover and extend several extrapolation theorems in the literature. Finally, we provide an application of our results to the Riesz potential and the Bilinear Hilbert transform.
