East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON A TWO WEIGHTS ESTIMATE FOR THE COMMUTATOR

  • Chung, Daewon (Faculty of Basic Sciences, Mathematics Major, Keimyung University)
  • Received : 2016.09.30
  • Accepted : 2017.01.31
  • Published : 2017.01.31
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Abstract

We provide quantitative two weight estimates for the commutator of the Hilbert transform under certain conditions on a pair of weights (u, v) and b in $Carl_{u,v}$. In [10] and [11], Bloom's inequality is shown in a modern setting, and the boundedness of the commutators is provided by assuming both weights u, v are $A_2$ and $b{\in}BMO_{\rho}$. In the present paper we show that the condition on b can be replaced by $Carl_{u,v}$ by using the joint $A^d_2$ condition.

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References

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