Comments on Lusin’s Conjecture and Carleson’s Proof for L2 Fourier Series
Comments on Lusin’s Conjecture and Carleson’s Proof for L2 Fourier Series
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评Lusin猜想和Carleson L2傅里叶级数证明
DOI：
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
R. A. Hunt
中科院分区：
文献类型：
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作者：
R. A. Hunt
1913 年 Lusin 提出猜想 50 多年后，L. Carleson 证明了每个 L2 函数的傅立叶级数收敛于 a.e.在本文中，我们将回顾卢辛提出猜想的工作，并呈现一些相关结果的历史发展。我们将跟踪卡尔森证明中使用的结果的发展，并简要说明它们是如何使用的。我们将看到共轭函数是卢辛猜想和卡尔森证明的核心。 Hardy-Littlewood 极大函数和其他极大函数在后期发展中发挥着重要作用。
More than fifty years after Lusin’s conjecture in 1913, L. Carleson proved the Fourier series of every L2 function converges a.e. In this paper we will review the work of Lusin which led to his conjecture and present an historical development of some related results. We will follow the development of results which are used in Carleson’s proof and briefly indicate how they are used. We will see that the conjugate function is central to both Lusin’s conjecture and Carleson’s proof. The Hardy-Littlewood maximal function and other maximal functions play important roles in the later development.