A weak type $(1,1)$ estimate for the Hilbert operator in higher-dimensional setting

2022

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DOI 10.4064/sm201201-4-11
Data confidence 70 medium
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Abstract

We obtain a weak type $(1,1)$ estimate for a higher-dimensional version of the Hilbert operator, answering an open problem by A. Osękowski [Ann. Probab. 45 (2017)]. In fact, we establish complete boundedness of this operator.