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arXiv · 1909.10897

The boundedness of the Hilbert transformation from one rearrangement invariant Banach space into another and applications

F. Sukochev·K. Tulenov·D. Zanin
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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.

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F. Sukochev, K. Tulenov, D. Zanin. 2019-09-22. The boundedness of the Hilbert transformation from one rearrangement invariant Banach space into another and applications. https://doi.org/10.1016/j.bulsci.2020.102943

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