A commutator theorem and weighted BMO
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- by Steven Bloom PDF
- Trans. Amer. Math. Soc. 292 (1985), 103-122 Request permission
Abstract:
The main result of this paper is a commutator theorem: If $\mu$ and $\lambda$ are ${A_p}$ weights, then the commutator $H$, ${M_b}$ is a bounded operator from ${L^p}(\mu )$ into ${L^p}(\lambda )$ if and only if $b \in {\operatorname {BMO} _{{{(\mu {\lambda ^{ - 1}})}^{1/p}}}}$. 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 ${L^p}$ estimate for BMO. Finally, the commutator theorem is used to obtain vector-valued weighted norm inequalities for the Hilbert transform.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 292 (1985), 103-122
- MSC: Primary 42A50; Secondary 42B20, 46E40, 47B47
- DOI: https://doi.org/10.1090/S0002-9947-1985-0805955-5
- MathSciNet review: 805955