多重线性平方函数和多重权重

Pub Date : 2019-01-13 DOI:10.7146/MATH.SCAND.A-105504

L. Grafakos, P. Mohanty, Saurabh Shrivastava

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引用次数: 1

摘要

本文证明了一类光滑多重线性平方函数关于多重线性$A_{\vec P}$权值的加权估计。特别地，我们建立了与等边长不相交立方体相关的光滑多线性平方函数的加权估计。因此，对于这类特殊的多元线性平方函数，我们对Benea和Bernicot(论坛数学)提出的问题给出了肯定的答案。Sigma 4, 2016, e26)关于光滑双线性平方函数的未加权估计。

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Multilinear square functions and multiple weights

In this paper we prove weighted estimates for a class of smooth multilinear square functions with respect to multilinear $A_{\vec P}$ weights. In particular, we establish weighted estimates for the smooth multilinear square functions associated with disjoint cubes of equivalent side-lengths. As a consequence, for this particular class of multilinear square functions, we provide an affirmative answer to a question raised by Benea and Bernicot (Forum Math. Sigma 4, 2016, e26) about unweighted estimates for smooth bilinear square functions.

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