齐型空间中分数次积分交换子的加权端点估计

Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (4): 922-931.

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Weighted End-point Estimates for Commutators of Fractional Integrals on Spaces of Homogeneous Type

LIU Zong-Guang¹, TIAN Mao-Qian²

1.Department of Mathematics, China University of Mining and Technology (Beijing), Beijing 100083;
2.Commercial School, Shihezi |University, Xinjiang Wujiaqu |831300

Received:2009-03-06 Revised:2010-01-11 Online:2010-07-25 Published:2010-07-25
Supported by:
教育部重点基金项目(108136)资助

Abstract

Abstract:

In this paper, it is established that the weighted end-point estimates for the commutator of fractional integrals on the spaces of homogenesous type, i.e.,
w({x∈X:|[b, I_α]f(x)|>t})≤Cψ(∫_X A(||b||_* |f(x)|/t Θ(w(x))dμ(x)),
where b ∈BMO(X, d, μ), A(t)=tlog(e+t), ψ(t)=[tlog(e+t^α]^1/1-α, Θ(t)=t^1-αlog(e+t^-α).

Key words: Fractional integral operator, Commutator, Spaces of homogeneous type, Fractional maximal operator, Fractional Orlicz , maximal operator

CLC Number:

42B20

LIU Zong-Guang, TIAN Mao-Qian. Weighted End-point Estimates for Commutators of Fractional Integrals on Spaces of Homogeneous Type[J].Acta mathematica scientia,Series A, 2010, 30(4): 922-931.

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Weighted End-point Estimates for Commutators of Fractional Integrals on Spaces of Homogeneous Type

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