Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (2): 441-449.doi: 10.1016/S0252-9602(18)30759-8

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SHARP BOUNDS FOR HARDY OPERATORS ON PRODUCT SPACES

Mingquan WEI1, Dunyan YAN2   

  1. 1. School of Mathematics and Statistics, Xinyang Normal University, Xinyang 464000, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2016-06-07 Revised:2017-06-23 Online:2018-04-25 Published:2018-04-25
  • Contact: Mingquan WEI E-mail:weimingquan11@mails.ucas.ac.cn
  • Supported by:

    The work is supported by NSFC (11471309, 11271162, and 11561062), Project of Henan Provincial Department of Education (18A110028), the Nanhu Scholar Program for Young Scholars of XYNU, and Doctoral Scientific Research Startup Fund of Xinyang Normal University (2016).

Abstract:

In this article, we obtain the sharp bounds from LP(Gn) to the space wLP(Gn) for Hardy operators on product spaces. More generally, the precise norms of Hardy operators on product spaces from LP(Gn) to the space LPI(Gn) are obtained.

Key words: Hardy operators, product spaces, wLP(Gn), LPI(Gn), norm

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