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- W4297978480 abstract "We show that if an operator T is bounded on weighted Lebesgue space L^2(w) and obeys a linear bound with respect to the A_2 constant of the weight, then its commutator [b,T] with a function b in BMO will obey a quadratic bound with respect to the A_2 constant of the weight. We also prove that the kth-order commutator T^k_b=[b,T^{k-1}_b] will obey a bound that is a power (k+1) of the A_2 constant of the weight. Sharp extrapolation provides corresponding L^p(w) estimates. The results are sharp in terms of the growth of the operator norm with respect to the A_p constant of the weight for all 1<p<infty, all k, and all dimensions, as examples involving the Riesz transforms, power functions and power weights show." @default.
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- W4297978480 date "2010-02-11" @default.
- W4297978480 modified "2023-10-03" @default.
- W4297978480 title "Sharp bounds for general commutators on weighted Lebesgue spaces" @default.
- W4297978480 doi "https://doi.org/10.48550/arxiv.1002.2396" @default.
- W4297978480 hasPublicationYear "2010" @default.
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