A weak type $(1,1)$ estimate for the Hilbert operator in higher-dimensional setting
Tom 265 / 2022
Studia Mathematica 265 (2022), 241-256
MSC: Primary 31B10, 47B38, 26B15, 46E30, 46A16, 47B01, 28B05, 46A32, 44A15; Secondary 46L51, 46L52.
DOI: 10.4064/sm201201-4-11
Opublikowany online: 11 April 2022
Streszczenie
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.
