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arXiv · 2402.05299

Boundedness of the Hilbert transform on weighted Lorentz spaces

Elona Agora·María J. Carro·Javier Soria
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Abstract

We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $Λ^p_u(w)$. We start by giving several necessary conditions that, in particular, lead us to the complete characterization of the weak-type boundedness of both $H$ and $H^*$, whenever $u\in A_1$. For the strong-type case, we also get the characterization of both operators when $p>1$. Applications to the case of Lorentz spaces $L^{p,q}(u)$ are presented.

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Elona Agora, María J. Carro, Javier Soria. 2024-02-07. Boundedness of the Hilbert transform on weighted Lorentz spaces. https://doi.org/10.1016/j.jmaa.2012.05.031

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