Abstract
We prove weighted strong inequalities for the multilinear potential operator \({\cal T}_{\phi}\) and its commutator, where the kernel ϕ satisfies certain growth condition. For these operators we also obtain Fefferman-Stein type inequalities and Coifman type estimates. Moreover we prove weighted weak type inequalities for the multilinear maximal operator \(\mathcal{M}_{\varphi,L^{B}}\) associated to an essentially nondecreasing function φ and to the Orlicz space L B for a given Young function B. This result allows us to obtain a weighted weak type inequality for the operator \({\cal T}_{\phi}\).
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The authors were supported by Consejo Nacional de Investigaciones Científicas y Técnicas and Universidad Nacional del Litoral.
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Bernardis, A., Gorosito, O. & Pradolini, G. Weighted Inequalities for Multilinear Potential Operators and their Commutators. Potential Anal 35, 253–274 (2011). https://doi.org/10.1007/s11118-010-9211-z
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DOI: https://doi.org/10.1007/s11118-010-9211-z