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.

中文翻译：

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多线性 Muckenhoupt 类的端点估计、外推和应用

在本文中，我们介绍了当前论文的第一、第二和第四作者最近的工作中宣布的结果，这些论文关于所谓的多线性 Muckenhoupt 类的 Rubio de Francia 外推。这里我们考虑出现在假设和/或结论中的勒贝格空间的一些指数可能是无穷大的情况。我们遵循的方案是相似的，但是在这样做时，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”案例，这是上述论文中的主要工具之一。本文的第二个目标是展示一些应用。例如，我们获得了双线性 Calderon-Zygmund 算子张量积的全范围混合范数估计值，证明是基于外推法和一些混合范数类中权重的估计值。多线性 Calderon-Zygmund 算子、双线性 Hilbert 变换和具有 BMO 函数的相应换向器也会发生同样的情况。外推以及已经建立的加权范数不等式很容易给出具有多重线性权重的标量和向量值不等式，其中包括端点情况。