A commutator theorem and weighted BMO

Author:
Steven Bloom

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

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Abstract | References | Similar Articles | Additional Information

Abstract: The main result of this paper is a commutator theorem: If and are weights, then the commutator , is a bounded operator from into if and only if . 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 estimate for BMO. Finally, the commutator theorem is used to obtain vector-valued weighted norm inequalities for the Hilbert transform.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1985-0805955-5

Article copyright:
© Copyright 1985
American Mathematical Society