Boundedness of the Hilbert transform on weighted Lorentz spaces

Autor: Agora, Elona, Carro, María J., Soria, Javier
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