Two-weight, weak-type norm inequalities for fractional integrals, Calderon-Zygmund operators and commutators
By D. Cruz-Uribe. 2000
75 citations recorded by the source corpus.
We give Ap-type conditions which are sucient for the two-weight, weak-type (p,p) inequalities for fractional integral operators, Calderon-Zygmund operators and commutators. For fractional integral operators, this solves a problem posed by Sawyer and Wheeden (28). At the heart of all of our proofs is an inequality relating the Hardy-Littlewood maximal function and the sharp maximal function which is strongly reminiscent of the good- inequality of Feerman and Stein (13).
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/2b01efea22cb53668a781d4e08db261dd1e17c16
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In Applied Mathematics
- Kabe Moen
- D. Cruz-Uribe
- Andrei K. Lerner
- Tuomas Hytönen
- C. P'erez
- P. Hasto
- Kangwei Li
- Michael T. Lacey
Citations in the corpus
- Two weight norm inequalities for fractional integral operators and commutators (2014, background): “h C(t) = t qlog(e+ t) 1+, and D(t) = tp0log(e+ t)2p0 , then the strong (p;q) inequality [b;I ](˙) : Lp(˙) !Lq(u) holds. There is no comparable result known for the weak (p;q) inequality. However, in [29] two weight weak type inequalities were proved for singular integral operators and we believe tha”
- One and two weight norm inequalities for Riesz potentials (2012, background): “8 was only known when Φ is power bump (see [1, 6]) or a log bump of the form Φ(t) = t log(e+ t).”