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

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. [ABSTRACT FROM AUTHOR]