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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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