ON A TWO WEIGHTS ESTIMATE FOR THE COMMUTATOR
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We provide quantitative two weight estimates for the commu- tator of the Hilbert transform under certain conditions on a pair of weights (u,v) and b in Carlu,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 A2 and b ∈ BMOρ. In the present paper we show that the condition on b can be replaced by Carlu,v by using the joint Ad2 condition.
Abstract
We provide quantitative two weight estimates for the commu- tator of the Hilbert transform under certain conditions on a pair of weights (u,v) and b in Carlu,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 A2 and b ∈ BMOρ. In the present paper we show that the condition on b can be replaced by Carlu,v by using the joint Ad2 condition.
참고문헌 (16)
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