The boundedness of the Hilbert transformation from one rearrangement invariant Banach space into another and applications
Sukochev F. Tulenov K. Zanin D.
March 2021Elsevier Masson s.r.l.
Bulletin des Sciences Mathematiques
2021#167
In this paper, we study the boundedness of the Hilbert transformation in Lorentz function spaces, thereby complementing classical results of Boyd. We also characterize the optimal range of a triangular truncation operator in Schatten-Lorentz ideals. These results further entail sharp commutator estimates and applications to operator Lipschitz functions in Schatten-Lorentz ideals.
Calderón operator , Hilbert transformation , Lorentz spaces , Optimal symmetric range , Schatten-Lorentz ideals , Triangular truncation operator
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School of Mathematics and Statistics, University of New South Wales, Kensington, 2052, NSW, Australia
Southern Mathematical Institute of Russian Academy of Science, Vladikavkaz, 362027, Russian Federation
Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
School of Mathematics and Statistics
Southern Mathematical Institute of Russian Academy of Science
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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