Morrey-Type Spaces on Gauss Measure Spaces and Boundedness of Singular Integrals

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• 作者：Liguang Liu (1)
  Yoshihiro Sawano (2)
  Dachun Yang (3)
  
• 关键词：Locally doubling measure space ; Gauss measure space ; Morrey space ; Campanato space ; Riesz transform ; Singular integral ; 42B35 ; 42B20 ; 42B25
• 刊名：Journal of Geometric Analysis
• 出版年：2014
• 出版时间：April 2014
• 年：2014
• 卷：24
• 期：2
• 页码：1007-1051
• 全文大小：597 KB
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• 作者单位：Liguang Liu (1)
  Yoshihiro Sawano (2)
  Dachun Yang (3)
  
  1. Department of Mathematics, School of Information, Renmin University of China, Beijing, 100872, People’s Republic of China
  2. Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan
  3. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People’s Republic of China
  
• ISSN：1559-002X

文摘

In this paper, the authors introduce Morrey-type spaces on the locally doubling metric measure spaces, which means that the underlying measure enjoys the doubling and the reverse doubling properties only on a class of admissible balls, and then obtain the boundedness of the local Hardy–Littlewood maximal operator and the local fractional integral operator on such Morrey-type spaces. These Morrey-type spaces on the Gauss measure space are further proved to be naturally adapted to singular integrals associated with the Ornstein–Uhlenbeck operator. To be precise, by means of the locally doubling property and the geometric properties of the Gauss measure, the authors establish the equivalence between Morrey-type spaces and Campanato-type spaces on the Gauss measure space, and the boundedness for a class of singular integrals associated with the Ornstein–Uhlenbeck operator (including Riesz transforms of any order) on Morrey-type spaces over the Gauss measure space.