Research Article

Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals

Published in: Quaestiones Mathematicae
Volume 46 , issue 4 , 2023 , pages: 813–831

DOI: 10.2989/16073606.2022.2043481

Author(s): K.S. Tulenov Al-Farabi Kazakh National University, Kazakhstan

Keywords: Primary: 46E30 , 47B10 , 46L51 , 46L52 , 44A15 , Secondary: 47L20 , 47C15 , Optimal range , Hilbert transform , triangular truncation operator , Calderón operator , Lorentz space , Schatten-Lorentz ideal

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Abstract

In this paper, it is investigated the optimal range of the classical Hilbert transform in Lorentz spaces of functions and its non-commutative counterparts including a triangular truncation operator in Schatten-Lorentz ideals. Some applications of obtained results to operator Lipschitz functions and commutator estimates in Schatten-Lorentz ideals of compact operators are presented.

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