Sharp Estimates for Potential Operators Associated with Laguerre and Dunkl-Laguerre Expansions

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• 作者：Adam Nowak ; Krzysztof Stempak
• 关键词：Laguerre Expansion ; Dunkl ; Laguerre Expansion ; Laguerre Operator ; Dunkl Harmonic Oscillator ; Negative Power ; Potential Operator ; Fractional Integral ; Potential Kernel ; Primary 42C10 ; 47G40 ; Secondary 31C15 ; 26A33
• 刊名：Potential Analysis
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：44
• 期：1
• 页码：109-136
• 全文大小：471 KB
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• 作者单位：Adam Nowak (1)
  Krzysztof Stempak (2)
  
  1. Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-656, Warszawa, Poland
  2. Wydział Matematyki, Politechnika Wrocławska, Wyb. Wyspiańskiego 27, 50–370, Wrocław, Poland
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X

文摘

We study potential operators associated with Laguerre function expansions of convolution and Hermite types, and with Dunkl-Laguerre expansions. We prove qualitatively sharp estimates of the corresponding potential kernels. Then we characterize those 1 ≤ p,q ≤ 8, for which the potential operators are L p - L q bounded. These results are sharp analogues of the classical Hardy-Littlewood-Sobolev fractional integration theorem in the Laguerre and Dunkl-Laguerre settings. Keywords Laguerre Expansion Dunkl-Laguerre Expansion Laguerre Operator Dunkl Harmonic Oscillator Negative Power Potential Operator Fractional Integral Potential Kernel