On a counterexample related to weighted weak type estimates for singular integrals
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- by Marcela Caldarelli, Andrei K. Lerner and Sheldy Ombrosi PDF
- Proc. Amer. Math. Soc. 145 (2017), 3005-3012 Request permission
Abstract:
We show that the Hilbert transform does not map $L^1(M_{\Phi }w)$ to $L^{1,\infty }(w)$ for every Young function $\Phi$ growing more slowly than $t\log \log (\textrm {e}^\textrm {e}+t)$. Our proof is based on a construction of M.C. Reguera and C. Thiele.References
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Additional Information
- Marcela Caldarelli
- Affiliation: Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
- Email: marcela.caldarelli@uns.edu.ar
- Andrei K. Lerner
- Affiliation: Department of Mathematics, Bar-Ilan University, 5290002 Ramat Gan, Israel
- MR Author ID: 615118
- Email: lernera@math.biu.ac.il
- Sheldy Ombrosi
- Affiliation: Departamento de Matemática, Universidad Nacional del Sur, Bahía Blanca, 8000, Argentina
- MR Author ID: 713193
- Email: sombrosi@uns.edu.ar
- Received by editor(s): July 9, 2015
- Received by editor(s) in revised form: August 11, 2016
- Published electronically: January 6, 2017
- Additional Notes: The second author was supported by the Israel Science Foundation (grant No. 953/13).
- Communicated by: Alexander Iosevich
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 3005-3012
- MSC (2010): Primary 42B20, 42B25
- DOI: https://doi.org/10.1090/proc/13496
- MathSciNet review: 3637948