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arXiv · 1506.08317

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

Marcela Caldarelli·Andrei K. Lerner·Sheldy Ombrosi
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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 $t\log\log ({\rm e}^{\rm e}+t)$. Our proof is based on a construction of M.C. Reguera and C. Thiele.

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Marcela Caldarelli, Andrei K. Lerner, Sheldy Ombrosi. 2015-06-27. On a counterexample related to weighted weak type estimates for singular integrals. https://arxiv.org/abs/1506.08317

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