End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
End-point estimates, extrapolation for multilinear Muckenhoupt classes, and applications
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多线性 Muckenhoupt 类的终点估计、外推以及应用
DOI：
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发表时间：
2019
期刊：
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通讯作者：
Emil Vuorinen
中科院分区：
文献类型：
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作者：
Kangwei Li;J. M. Martell;Henri Martikainen;S. Ombrosi;Emil Vuorinen
在本文中，我们提出的结果宣布在最近的工作中的第一，第二，第四作者的当前文件有关鲁比奥德弗朗西亚外推所谓的多线性Muckenhoupt类。在这里，我们考虑的情况下，一些指数的勒贝格空间出现在假设和/或结论可能是无穷大。我们遵循的方案是类似的，但是，在这样做的时候，我们需要开发一个单变量端点非对角外推结果。这补充了Duoandikoetxea获得的相应“有限”情况，这是上述论文中的主要工具之一。本文的第二个目标是介绍一些应用程序。例如，我们得到了全范围的混合范数估计的双线性Calderon-Zygmund算子的张量积的证明的基础上外推和一些估计的权重在一些混合范数类。多线性Calderon-Zygmund算子、双线性希尔伯特变换和相应的BMO函数的分解算子也是如此。外推沿着已经建立的加权范数不等式很容易得到多线性权重的标量和向量值不等式，这些包括端点的情况。
In this paper we present the results announced in the recent work by the first, second, and fourth authors of the current paper concerning Rubio de Francia extrapolation for the so-called multilinear Muckenhoupt classes. Here we consider the situations where some of the exponents of the Lebesgue spaces appearing in the hypotheses and/or in the conclusion can be possibly infinity. The scheme we follow is similar, but, in doing that, we need to develop a one-variable end-point off-diagonal extrapolation result. This complements the corresponding "finite" case obtained by Duoandikoetxea, which was one of the main tools in the aforementioned paper. The second goal of this paper is to present some applications. For example, we obtain the full range of mixed-norm estimates for tensor products of bilinear Calderon-Zygmund operators with a proof based on extrapolation and on some estimates with weights in some mixed-norm class. The same occurs with the multilinear Calderon-Zygmund operators, the bilinear Hilbert transform, and the corresponding commutators with BMO functions. Extrapolation along with the already established weighted norm inequalities easily give scalar and vector-valued inequalities with multilinear weights and these include the end-point cases.