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›› 2016, Vol. 33 ›› Issue (4): 433-437.DOI: 10.7523/j.issn.2095-6134.2016.04.001

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Sharp bounds for generalized Hardy operator on product space

WEI Mingquan, YAN Dunyan   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-12-02 Revised:2016-01-04 Online:2016-07-15
  • Supported by:

    Supported by the National Nature Science Foundation of China (11471309, 11271162, 11561062)

Abstract:

We characterize a sufficient and necessary condition which ensures that the generalized Hardy operator Uψf(x)=f(x1t1,…,xntn)ψ(t1,…,tn)dt1dtn is bounded on RMO(Rn).The condition deeply depends on the nonnegative function ψ defined on [0,1]×…×[0,1].Furthermore, the corresponding operator norm is worked out.In addition, we also extend the results to the high-dimensional product space.

Key words: generalized Hardy operator, product space, RMO(Rn)

CLC Number: