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A Commutator Theorem and Weighted BMO

Steven Bloom
Transactions of the American Mathematical Society
Vol. 292, No. 1 (Nov., 1985), pp. 103-122
DOI: 10.2307/2000172
Stable URL: http://www.jstor.org/stable/2000172
Page Count: 20
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A Commutator Theorem and Weighted BMO
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Abstract

The main result of this paper is a commutator theorem: If μ and λ are Ap weights, then the commutator H, Mb is a bounded operator from Lp(μ) into Lp(λ) if and only if b ∈ BMO(μ λ-1)1/p . The proof relies heavily on a weighted sharp function theorem. Along the way, several other applications of this theorem are derived, including a doubly-weighted Lp estimate for BMO. Finally, the commutator theorem is used to obtain vector-valued weighted norm inequalities for the Hilbert transform.

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