SHARP BOUNDS FOR GENERAL COMMUTATORS ON WEIGHTED LEBESGUE SPACES
By Daewon Chung, C. Pereyra, C. P'erez. 2010
79 citations recorded by the source corpus.
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 A2 constant of the weight, then its commutator (b;T ) with a function b in BMO will obey a quadratic bound with respect to the A2 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 A2 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 Ap constant of the weight for all 1 < p <1, all k, and all dimensions, as examples involving the Riesz transforms, power functions and power weights show.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/980406defd0226269675bd31a3d1bb5e53c10700
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In Applied Mathematics
- D. Cruz-Uribe
- Andrei K. Lerner
- Kabe Moen
- Tuomas Hytönen
- C. P'erez
- P. Hasto
- Dachun Yang
- J. M. Martell
In Mathematical Physics
Citations in the corpus
- On pointwise and weighted estimates for commutators of Calder\'on-Zygmund operators (2016, unknown): “Pérez [3]: ‖[b, T ]‖Lp(w) ≤ c(n, p, T )‖b‖BMO[w] 2 max ( 1, 1 p−1 ) Ap (1 < p < ∞) (1.”
- Two weight norm inequalities for fractional integral operators and commutators (2014, methodology): “This was proved in [23] using a Cauchy integral formula technique due to Chung, Pereyra and Pérez [11].”