Sharp bounds for generalized Hardy operator on product space
Received date: 2015-12-02
Revised date: 2016-01-04
Online published: 2016-07-15
Supported by
Supported by the National Nature Science Foundation of China (11471309, 11271162, 11561062)
魏明权 , 燕敦验 . 乘积空间上的广义哈代算子的有界性[J]. 中国科学院大学学报, 2016 , 33(4) : 433 -437 . DOI: 10.7523/j.issn.2095-6134.2016.04.001
We characterize a sufficient and necessary condition which ensures that the generalized Hardy operator Uψf(x)=
f(x1t1,…,xntn)ψ(t1,…,tn)dt1…dtn 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)
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f（x1t1，…，xntn）ψ（t1，…，tn）dt1…dtn在RMO（Rn）上有界的充分必要条件，这个条件完全依赖于定义在[0，1]×…×[0，1]上的非负函数ψ。还给出了Uψ的算子范数。此外，还把这个结果推广到高维乘积空间。