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

Kanat Tulenov (UGent)
(2022) QUAESTIONES MATHEMATICAE. 46(4). p.813-831
Author
Organization
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.
Keywords
Primary, Secondary, Optimal range, Hilbert transform, triangular truncation operator, Calderon operator, Lorentz space, Schatten-Lorentz ideal, SOBOLEV IMBEDDINGS, RANGE, COMMUTATOR, LIPSCHITZ

Citation

Please use this url to cite or link to this publication:

MLA
Tulenov, Kanat. “Boundedness of the Hilbert Transform in Lorentz Spaces and Applications to Operator Ideals.” QUAESTIONES MATHEMATICAE, vol. 46, no. 4, 2022, pp. 813–31, doi:10.2989/16073606.2022.2043481.
APA
Tulenov, K. (2022). Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals. QUAESTIONES MATHEMATICAE, 46(4), 813–831. https://doi.org/10.2989/16073606.2022.2043481
Chicago author-date
Tulenov, Kanat. 2022. “Boundedness of the Hilbert Transform in Lorentz Spaces and Applications to Operator Ideals.” QUAESTIONES MATHEMATICAE 46 (4): 813–31. https://doi.org/10.2989/16073606.2022.2043481.
Chicago author-date (all authors)
Tulenov, Kanat. 2022. “Boundedness of the Hilbert Transform in Lorentz Spaces and Applications to Operator Ideals.” QUAESTIONES MATHEMATICAE 46 (4): 813–831. doi:10.2989/16073606.2022.2043481.
Vancouver
1.
Tulenov K. Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals. QUAESTIONES MATHEMATICAE. 2022;46(4):813–31.
IEEE
[1]
K. Tulenov, “Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals,” QUAESTIONES MATHEMATICAE, vol. 46, no. 4, pp. 813–831, 2022.
@article{01H0339TM4RVRAJ0F7DG3XE800,
  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.}},
  author       = {{Tulenov, Kanat}},
  issn         = {{1607-3606}},
  journal      = {{QUAESTIONES MATHEMATICAE}},
  keywords     = {{Primary,Secondary,Optimal range,Hilbert transform,triangular truncation operator,Calderon operator,Lorentz space,Schatten-Lorentz ideal,SOBOLEV IMBEDDINGS,RANGE,COMMUTATOR,LIPSCHITZ}},
  language     = {{eng}},
  number       = {{4}},
  pages        = {{813--831}},
  title        = {{Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals}},
  url          = {{http://doi.org/10.2989/16073606.2022.2043481}},
  volume       = {{46}},
  year         = {{2022}},
}
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