\(\mathcal {A}_{p, {\mathbb {E}}}\) Weights, Maximal Operators, and Hardy Spaces Associated with a Family of General Sets
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- 作者：Yong Ding (1)
Ming-Yi Lee (2)
Chin-Cheng Lin (2) - 关键词：$$A_p$$ A p weights ; BMO ; Hardy spaces ; maximal operator ; Primary 42B25 ; 42B30 ; Secondary 35B45
- 刊名：Journal of Fourier Analysis and Applications
- 出版年：2014
- 出版时间：June 2014
- 年：2014
- 卷：20
- 期：3
- 页码：608-667
- 全文大小：
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Ming-Yi Lee (2)
Chin-Cheng Lin (2)
1. School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing Normal University, Beijing, 100875, China
2. Department of Mathematics, National Central University, Chung-Li, 320, Taiwan - ISSN：1531-5851
文摘
Suppose that \({\mathbb {E}}:=\{E_r(x)\}_{r\in {\mathcal {I}}, x\in X}\) is a family of open subsets of a topological space \(X\) endowed with a nonnegative Borel measure \(\mu \) satisfying certain basic conditions. We establish an \(\mathcal {A}_{{\mathbb {E}}, p}\) weights theory with respect to \({\mathbb {E}}\) and get the characterization of weighted weak type (1,1) and strong type \((p,p)\) , \(1<p\le \infty \) , for the maximal operator \({\mathcal {M}}_{{\mathbb {E}}}\) associated with \({\mathbb {E}}\) . As applications, we introduce the weighted atomic Hardy space \(H^1_{{\mathbb {E}}, w}\) and its dual \(BMO_{{\mathbb {E}},w}\) , and give a maximal function characterization of \(H^1_{{\mathbb {E}},w}\) . Our results generalize several well-known results.