The boundedness of the Hilbert transformation from one rearrangement invariant Banach space into another and applications
arXiv:1909.10897 · doi:10.1016/j.bulsci.2020.102943
Abstract
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.
17. arXiv admin note: text overlap with arXiv:1908.09548