On the sharp upper bound related to the weak Muckenhoupt–Wheeden conjecture

Andrei K. Lerner, Fëdor Nazarov, Sheldy Ombrosi

Type: Article

Publication Date: 2020-09-12

Citations: 16

DOI: https://doi.org/10.2140/apde.2020.13.1939

Abstract

We construct an example showing that the upper bound $[w]_{A_1}\log({\rm{e}}+[w]_{A_1})$ for the $L^1(w)\to L^{1,\infty}(w)$ norm of the Hilbert transform cannot be improved in general.

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+	A Bellman function counterexample to the $A_1$ conjecture: the blow-up of the weak norm estimates of weighted singular operators	2015	Fëdor Nazarov Alexander Reznikov Vasily Vasyunin Alexander Volberg
+	Some Maximal Inequalities	1971	Charles Fefferman E. M. Stein
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