Boundedness of the Hilbert transform on weighted Lorentz spaces
Autor: | Agora, Elona, Carro, María J., Soria, Javier |
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Rok vydání: | 2024 |
Předmět: | |
Zdroj: | J. Math. Anal. Appl. (2012) |
Druh dokumentu: | Working Paper |
DOI: | 10.1016/j.jmaa.2012.05.031 |
Popis: | We study the boundedness of the Hilbert transform $H$ and the Hilbert maximal operator $H^*$ on weighted Lorentz spaces $\Lambda^p_u(w)$. 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. Comment: 17 pages |
Databáze: | arXiv |
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