Square Function Characterization of Weak Hardy Spaces

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• 作者：Danqing He (1)
  
• 关键词：Hardy and weak Hardy spaces ; weak $$L^p$$ L p spaces ; Interpolation ; Primary 42B30 ; Secondary 42B35
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2014
• 出版时间：October 2014
• 年：2014
• 卷：20
• 期：5
• 页码：1083-1110
• 全文大小：495 KB
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• 作者单位：Danqing He (1)
  
  1. Department of Mathematics, University of Missouri, Columbia, MO聽, 65211, USA
  
• ISSN：1531-5851

文摘

We obtain a new square function characterization of the weak Hardy space \(H^{p,\infty }\) for all \(p\in (0,\infty )\) . This space consists of all tempered distributions whose smooth maximal function lies in weak \(L^p\) . Our proof is based on interpolation between \(H^p\) spaces. The main difficulty we overcome is the lack of a good dense subspace of \(H^{p,\infty }\) which forces us to work with general \(H^{p,\infty }\) distributions.