具有矩阵权重的锐平方函数估计

IF 1 3区数学 Q1 MATHEMATICS

Discrete Analysis Pub Date : 2017-02-15 DOI:10.19086/da.7597

T. Hytonen, S. Petermichl, A. Volberg

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引用次数: 24

摘要

我们证明了二进平方函数的矩阵$A_2$猜想，即矩阵加权平方函数的范数估计，其中重点是估计中对矩阵$A_2*常数的尖锐线性依赖性。此外，我们给出了$a_2$和$a_｛\infty｝$常数的混合估计。关键是受矩阵加权平方函数的积分形式启发，对一个过程进行稀疏控制。

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The sharp square function estimate with matrix weight

We prove the matrix $A_2$ conjecture for the dyadic square function, that is, a norm estimate of the matrix weighted square function, where the focus is on the sharp linear dependence on the matrix $A_2$ constant in the estimate. Moreover, we give a mixed estimate in terms of $A_2$ and $A_{\infty}$ constants. Key is a sparse domination of a process inspired by the integrated form of the matrix--weighted square function.

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来源期刊

Discrete Analysis Mathematics-Algebra and Number Theory

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

17 weeks

期刊介绍： Discrete Analysis is a mathematical journal that aims to publish articles that are analytical in flavour but that also have an impact on the study of discrete structures. The areas covered include (all or parts of) harmonic analysis, ergodic theory, topological dynamics, growth in groups, analytic number theory, additive combinatorics, combinatorial number theory, extremal and probabilistic combinatorics, combinatorial geometry, convexity, metric geometry, and theoretical computer science. As a rough guideline, we are looking for papers that are likely to be of genuine interest to the editors of the journal.