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

Bar-Ilan University

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

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

Keywords

Hilbert transform
Weak type estimates
Weights

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/proc/13496

Cite this

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title = "On a counterexample related to weighted weak type estimates for singular integrals",

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

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AU - Caldarelli, Marcela

AU - Lerner, Andrei K.

AU - Ombrosi, Sheldy

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

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KW - Weights

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U2 - 10.1090/proc/13496

DO - 10.1090/proc/13496

M3 - مقالة

SN - 0002-9939

VL - 145

SP - 3005

EP - 3012

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 7

ER -

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

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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