Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals
Tulenov K.S.
2023Taylor and Francis Ltd.
Quaestiones Mathematicae
2023#46Issue 4813 - 831 pp.
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.
Calderón operator , Hilbert transform , Lorentz space , Optimal range , Schatten-Lorentz ideal , triangular truncation operator
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Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University
Institute of Mathematics and Mathematical Modeling
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