Abstract
Necessary and sufficient conditions are given for generalized Calderón and Hilbert operators to be bounded from weighted Lebesgue spaces into suitable weighted BMO and Lipschitz spaces. Moreover, we have obtained new results on the boundedness of these operators from \(L^{\infty }\) into BMO, even in the unweighted case for the Hilbert operator. The class of weights involved are close to the doubling and reverse Hölder conditions related to the Muckenhoupt’s classes.
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This research was partially supported by grants from CONICET (Argentina), SeCyT (Universidad Nacional de Córdoba) and the Universidad Nacional del Litoral.
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Ferreyra, E.V., Flores, G.J. & Viviani, B.E. Weighted Lebesgue and \(BMO^\gamma \) norm inequalities for the Calderón and Hilbert operators. Math. Z. 294, 503–518 (2020). https://doi.org/10.1007/s00209-019-02298-6
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DOI: https://doi.org/10.1007/s00209-019-02298-6