Martingale Transforms and the Hardy-Littlewood-Sobolev Inequality for Semigroups

详细信息    查看全文

• 作者：Daesung Kim
• 关键词：Martingale transform ; The Hardy ; Littlewood ; Paley inequality ; Fractional integrals ; The Littlewood ; Paley g ; functions ; General Markovian semigroups
• 刊名：Potential Analysis
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：45
• 期：4
• 页码：795-807
• 全文大小：262 KB
• 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
• 卷排序：45

文摘

We give a representation of the fractional integral for symmetric Markovian semigroups as the projection of martingale transforms and prove the Hardy-Littlewood-Sobolev (HLS) inequality based on this representation. The proof rests on a new inequality for the fractional Littlewood-Paley g–function.