Weak and Strong Type A 1 –A ∞ Estimates for Sparsely Dominated Operators

Title

Weak and Strong Type A 1 –A ∞ Estimates for Sparsely Dominated Operators

 Author

Frey, D. (TU Delft Analysis)
Nieraeth, Z. (TU Delft Analysis) ORCID 0000-0002-5907-5336

 Date

2018

 Abstract

We consider operators T satisfying a sparse domination property (Formula presented.)with averaging exponents (Formula presented.). We prove weighted strong type boundedness for (Formula presented.) and use new techniques to prove weighted weak type (Formula presented.) boundedness with quantitative mixed (Formula presented.)–(Formula presented.) estimates, generalizing results of Lerner, Ombrosi, and Pérez and Hytönen and Pérez. Even in the case (Formula presented.) we improve upon their results as we do not make use of a Hörmander condition of the operator T. Moreover, we also establish a dual weak type (Formula presented.) estimate. In a last part, we give a result on the optimality of the weighted strong type bounds including those previously obtained by Bernicot, Frey, and Petermichl.


 Subject

Muckenhoupt weights
Sharp weighted bounds
Sparse domination

 To reference this document use:

http://resolver.tudelft.nl/uuid:e5214706-d5e2-467c-996a-8c3722a3242b

 DOI

https://doi.org/10.1007/s12220-018-9989-2

 ISSN

1050-6926

 Source

Journal of Geometric Analysis, 29 (2019), 247–282

 Part of collection

Institutional Repository

 Document type

journal article

 Rights

© 2018 D. Frey, Z. Nieraeth
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