Sharp weighted bounds without testing or extrapolation

By Kabe Moen. 2012

75 citations recorded by the source corpus.

We give a short proof of the sharp weighted bound for sparse operators that holds for all p,1 < p < ∞. By recent developments this implies the bounds hold for any Calderón–Zygmund operator. The novelty of our approach is that we avoid two techniques that are present in other proofs: two weight inequalities and extrapolation. Our techniques are applicable to fractional integral operators as well.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/50ecc7c5e36f5cf9854ef802835feacb42d72102

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In Applied Mathematics

1. D. Cruz-Uribe
2. Kabe Moen
3. Kangwei Li
4. Andrei K. Lerner
5. Wenchang Sun
6. Sfo
7. Tuomas Hytönen
8. C. P'erez

Citations in the corpus

• A Fractional Muckenhoupt–Wheeden Theorem and its Consequences (2013, background): “The operator M D β satisfies norm inequalities with bounds independent of μ: the proof of the next result can be found in [21].”
• On pointwise estimates involving sparse operators (2015, background): “The following lemma is well known (its variations and extensions can be found in [3, 8, 12, 13]).”
• The Sharp Weighted Bound for Multilinear Maximal Functions and Calderón–Zygmund Operators (2012, methodology): “1) we refer the readers to [19] for a proof.”