On a counterexample related to weighted weak type estimates for singular integrals

Marcela Caldarelli; Andrei K. Lerner; Sheldy Ombrosi

doi:10.1090/proc/13496

On a counterexample related to weighted weak type estimates for singular integrals

Marcela Caldarelli
, Andrei K. Lerner
, Sheldy Ombrosi

Department of Mathematics

Universidad Nacional del Sur

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

We show that the Hilbert transform does not map L¹(M_Φw) to L^1,∞(w) for every Young function Φ growing more slowly than t log log(e^e +t). Our proof is based on a construction of M.C. Reguera and C. Thiele.

Original language	English
Pages (from-to)	3005-3012
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	7
DOIs	https://doi.org/10.1090/proc/13496
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 American Mathematical Society.

Funding

The second author was supported by the Israel Science Foundation (grant No. 953/13).

Funders	Funder number
Israel Science Foundation	953/13

Keywords

Hilbert transform
Weak type estimates
Weights

Access to Document

10.1090/proc/13496

Cite this

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KW - Weights

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On a counterexample related to weighted weak type estimates for singular integrals

Abstract

Bibliographical note

Funding

Keywords

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