L2-Lp estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group
- Author
- Vishvesh Kumar (UGent) and Shyam Swarup Mondal
- Organization
- Project
- Abstract
- In this paper, we study some operator theoretical properties of pseudo-differential operators with operator-valued symbols on the Heisenberg motion group. Specifically, we investigate L-2-L-p boundedness of pseudo-differential operators on the Heisenberg motion group for the range 2 <= p <= infinity. We also provide a necessary and sufficient condition on the operator-valued symbols in terms of lambda-Weyl transforms such that the corresponding pseudo-differential operators on the Heisenberg motion group are in the class of Hilbert-Schmidt operators. As a consequence, we obtain a characterization of the trace class pseudo-differential operators on the Heisenberg motion group and provide a trace formula for these trace class operators.
- Keywords
- Applied Mathematics, Analysis, Pseudo-differential operators, Heisenberg motion group, lambda-Weyl transforms, trace class operators, Hilbert-Schmidt operators, L-P-NUCLEARITY, PSEUDODIFFERENTIAL-OPERATORS, COMPACT, TRACES
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8754593
- MLA
- Kumar, Vishvesh, and Shyam Swarup Mondal. “L2-Lp Estimates and Hilbert–Schmidt Pseudo Differential Operators on the Heisenberg Motion Group.” APPLICABLE ANALYSIS, vol. 102, no. 13, 2023, pp. 3533–48, doi:10.1080/00036811.2022.2078717.
- APA
- Kumar, V., & Mondal, S. S. (2023). L2-Lp estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group. APPLICABLE ANALYSIS, 102(13), 3533–3548. https://doi.org/10.1080/00036811.2022.2078717
- Chicago author-date
- Kumar, Vishvesh, and Shyam Swarup Mondal. 2023. “L2-Lp Estimates and Hilbert–Schmidt Pseudo Differential Operators on the Heisenberg Motion Group.” APPLICABLE ANALYSIS 102 (13): 3533–48. https://doi.org/10.1080/00036811.2022.2078717.
- Chicago author-date (all authors)
- Kumar, Vishvesh, and Shyam Swarup Mondal. 2023. “L2-Lp Estimates and Hilbert–Schmidt Pseudo Differential Operators on the Heisenberg Motion Group.” APPLICABLE ANALYSIS 102 (13): 3533–3548. doi:10.1080/00036811.2022.2078717.
- Vancouver
- 1.Kumar V, Mondal SS. L2-Lp estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group. APPLICABLE ANALYSIS. 2023;102(13):3533–48.
- IEEE
- [1]V. Kumar and S. S. Mondal, “L2-Lp estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group,” APPLICABLE ANALYSIS, vol. 102, no. 13, pp. 3533–3548, 2023.
@article{8754593,
abstract = {{In this paper, we study some operator theoretical properties of pseudo-differential operators with operator-valued symbols on the Heisenberg motion group. Specifically, we investigate L-2-L-p boundedness of pseudo-differential operators on the Heisenberg motion group for the range 2 <= p <= infinity. We also provide a necessary and sufficient condition on the operator-valued symbols in terms of lambda-Weyl transforms such that the corresponding pseudo-differential operators on the Heisenberg motion group are in the class of Hilbert-Schmidt operators. As a consequence, we obtain a characterization of the trace class pseudo-differential operators on the Heisenberg motion group and provide a trace formula for these trace class operators.}},
author = {{Kumar, Vishvesh and Mondal, Shyam Swarup}},
issn = {{0003-6811}},
journal = {{APPLICABLE ANALYSIS}},
keywords = {{Applied Mathematics,Analysis,Pseudo-differential operators,Heisenberg motion group,lambda-Weyl transforms,trace class operators,Hilbert-Schmidt operators,L-P-NUCLEARITY,PSEUDODIFFERENTIAL-OPERATORS,COMPACT,TRACES}},
language = {{eng}},
number = {{13}},
pages = {{3533--3548}},
title = {{L2-Lp estimates and Hilbert–Schmidt pseudo differential operators on the Heisenberg motion group}},
url = {{http://doi.org/10.1080/00036811.2022.2078717}},
volume = {{102}},
year = {{2023}},
}
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