Abstract
We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including L2-Lq, Lq-BMO and L2-Lipschitz estimates. The kernels of such operators satisfy certain size condition and a Lipschitz type regularity, and the symbol of the commutator belongs to a Lipschitz class. We also deal with commutators of fractional type operators with less regular kernels satisfying a Hörmander’s type inequality. As far as we know, these last results are new even in the unweighted case. Moreover, we give a characterization result involving symbols of the commutators and continuity results for extreme values of p.
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Estefanía, D., Pradolini, G. & Ramos, W. The Effect of the Smoothness of Fractional Type Operators Over Their Commutators with Lipschitz Symbols on Weighted Spaces. FCAA 21, 628–653 (2018). https://doi.org/10.1515/fca-2018-0034
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DOI: https://doi.org/10.1515/fca-2018-0034