Characterization of the Weak-Type Boundedness of the Hilbert Transform on Weighted Lorentz Spaces |
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Authors: | Elona Agora María J Carro Javier Soria |
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Institution: | 1. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08007, Barcelona, Spain
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Abstract: | 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 . |
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