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Elona Agora María J. Carro Javier Soria 《Journal of Fourier Analysis and Applications》2013,19(4):712-730
We characterize the weak-type boundedness of the Hilbert transform H on weighted Lorentz spaces $\varLambda^{p}_{u}(w)$ , with p>0, in terms of some geometric conditions on the weights u and w and the weak-type boundedness of the Hardy–Littlewood maximal operator on the same spaces. Our results recover simultaneously the theory of the boundedness of H on weighted Lebesgue spaces L p (u) and Muckenhoupt weights A p , and the theory on classical Lorentz spaces Λ p (w) and Ariño-Muckenhoupt weights B p . 相似文献
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Elona Agora Jorge Antezana María J. Carro 《Journal of Fourier Analysis and Applications》2016,22(6):1431-1439
The main goal of this paper is to provide a characterization of the weak-type boundedness of the Hardy–Littlewood maximal operator, M, on weighted Lorentz spaces \(\Lambda ^p_u(w)\), whenever \(p>1\). This solves a problem left open in (Carro et al., Mem Am Math Soc. 2007). Moreover, with this result, we complete the program of unifying the study of the boundedness of M on weighted Lebesgue spaces and classical Lorentz spaces, which was initiated in the aforementioned monograph. 相似文献
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