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

Volume 265 / 2022

F. Sukochev, K. Tulenov, D. Zanin 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 Published online: 11 April 2022

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.

Authors

  • F. SukochevSchool of Mathematics and Statistics
    University of New South Wales
    Kensington, NSW, 2052, Australia
    e-mail
  • K. TulenovAl-Farabi Kazakh National University
    Almaty, 050040, Kazakhstan
    and
    Institute of Mathematics
    and Mathematical Modeling
    Almaty, 050010, Kazakhstan
    e-mail
  • D. ZaninSchool of Mathematics and Statistics
    University of New South Wales
    Kensington, NSW, 2052, Australia
    e-mail

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