\(L^{p}(\mu ) \rightarrow L^{q}(\nu )\) Characterization for Well Localized Operators

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• 作者：Emil Vuorinen
• 关键词：Well localized operator ; Two weight inequality ; Testing condition
• 刊名：Journal of Fourier Analysis and Applications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：22
• 期：5
• 页码：1059-1075
• 全文大小：620 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Fourier Analysis
  Abstract Harmonic Analysis
  Approximations and Expansions
  Partial Differential Equations
  Applications of Mathematics
  Signal,Image and Speech Processing
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5851
• 卷排序：22

文摘

We consider a two weight \(L^{p}(\mu ) \rightarrow L^{q}(\nu )\)-inequality for well localized operators as defined and studied by Nazarov et al. (Math Res Lett 15(3):583–597, 2008) when \(p=q=2\). A counterexample of Nazarov shows that the direct analogue of the results in Nazarov et al. (Math Res Lett 15(3):583–597, 2008) fails for \(p=q\not =2\). Here a new square function testing condition is introduced and applied to characterize the two weight norm inequality. The use of the square function testing condition is also demonstrated in connection with certain positive dyadic operators.