Variable martingale Hardy spaces and their applications in Fourier analysis
Variable martingale Hardy spaces and their applications in Fourier analysis
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DOI：
10.4064/dm807-12-2019
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发表时间：
2020-01-01
影响因子：
1.8
通讯作者：
Zhou, Dejian
中科院分区：
文献类型：
--
作者：
Jiao, Yong;Weisz, Ferenc;Zhou, Dejian
令p（.）是定义在概率空间上的可测函数，满足0 < p（-）：= ess inf（x是Ω的元素）p（x）1/2，条件1/p（-）- 1/P+ < 1成立。令人惊讶的是，这最后一个条件不出现三角傅立叶级数。证明的关键之一是引入了两个新的并元极大算子，并证明了它们在L-p（.）p（-）> 1。我们用来证明这些结果的方法是新的，即使在经典的情况下。由此得到了关于费耶尔平均的几乎处处收敛性和范数收敛性定理。
Let p(.) be a measurable function defined on a probability space satisfying0 < p(-) := ess inf(x is an element of Omega) p(x) 1/2 and the condition 1/p(-) - 1/P+ < 1 holds. It is surprising that this last condition does not appear for trigonometric Fourier series. One of the key points of the proof is that we introduce two new dyadic maximal operators and prove their boundedness on L-p(.) with p(-) > 1. The method we use to prove these results is new even in the classical case. As a consequence, we obtain theorems about almost everywhere and norm convergence of Fejer means.