Lp-Bounds of a class of mean operators on product spaces

CHEN Guangzhou; WEI Mingquan; YAN Dunyan

doi:10.7523/j.issn.2095-6134.2015.04.002

Journal of University of Chinese Academy of Sciences >

2015 , Vol. 32 >Issue 4: 437 - 440

DOI: https://doi.org/10.7523/j.issn.2095-6134.2015.04.002

L^p-Bounds of a class of mean operators on product spaces

CHEN Guangzhou ,
WEI Mingquan ,
YAN Dunyan

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College of Mathematica Science, University of Chinese Academy of Sciences, Beijing 100049

Received date: 2014-12-24

Revised date: 2015-01-09

Online published: 2015-07-15

Supported by

Supported by the National Nature Science Foundation of China (11471039, 11271162) 

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Abstract

We characterize a sufficient and necessary condition which ensures that the operator
H_φf(x)=...f(x₁ t₁,…,x_n t_nφ(t₁,…,t_n)dt₁…dt_n
is bounded on L^p(Gⁿ) with 1≤p≤∞. The condition deeply depends on the nonnegative function φ defined on [0,1]×…×[0,1]. Furthermore, the corresponding operator norms are worked out.

Key words： Hardy operator; product space; L^p

Cite this article

CHEN Guangzhou , WEI Mingquan , YAN Dunyan . L^p-Bounds of a class of mean operators on product spaces[J]. Journal of University of Chinese Academy of Sciences, 2015 , 32(4) : 437 -440 . DOI: 10.7523/j.issn.2095-6134.2015.04.002

References

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