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Nuclearity of operators related to finite measure spaces

Vishvesh Kumar (UGent) and Shyam Swarup Mondal
(2020) JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. 11(3). p.1031-1058
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Abstract
Let (S, B, in) be a finite measure space. The aim of this paper is to give necessary and sufficient conditions on symbols such that the corresponding Z-operators from L-p1 (Z) into L(p)2 (Z) and S-operators from L-p1 (S) into L-p2 (S) to be nuclear for 1 <= p1, p2 < infinity. We show that the adjoint of the nuclear Z-operator from L-p2' into L-p1' is again a nuclear operator. As applications, we get the symbol of the product of the nuclear operators with bounded operators.
Keywords
Pseudo-differential operators, Finite measure space, Fourier transform, S-operators, Z-operators, L-P-NUCLEARITY, PSEUDODIFFERENTIAL-OPERATORS, COMPACT, HAUSDORFF, ADJOINTS, TRACES

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MLA
Kumar, Vishvesh, and Shyam Swarup Mondal. “Nuclearity of Operators Related to Finite Measure Spaces.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, vol. 11, no. 3, 2020, pp. 1031–58, doi:10.1007/s11868-020-00353-z.
APA
Kumar, V., & Mondal, S. S. (2020). Nuclearity of operators related to finite measure spaces. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 11(3), 1031–1058. https://doi.org/10.1007/s11868-020-00353-z
Chicago author-date
Kumar, Vishvesh, and Shyam Swarup Mondal. 2020. “Nuclearity of Operators Related to Finite Measure Spaces.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 11 (3): 1031–58. https://doi.org/10.1007/s11868-020-00353-z.
Chicago author-date (all authors)
Kumar, Vishvesh, and Shyam Swarup Mondal. 2020. “Nuclearity of Operators Related to Finite Measure Spaces.” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 11 (3): 1031–1058. doi:10.1007/s11868-020-00353-z.
Vancouver
1.
Kumar V, Mondal SS. Nuclearity of operators related to finite measure spaces. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS. 2020;11(3):1031–58.
IEEE
[1]
V. Kumar and S. S. Mondal, “Nuclearity of operators related to finite measure spaces,” JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, vol. 11, no. 3, pp. 1031–1058, 2020.
@article{8688347,
  abstract     = {{Let (S, B, in) be a finite measure space. The aim of this paper is to give necessary and sufficient conditions on symbols such that the corresponding Z-operators from L-p1 (Z) into L(p)2 (Z) and S-operators from L-p1 (S) into L-p2 (S) to be nuclear for 1 <= p1, p2 < infinity. We show that the adjoint of the nuclear Z-operator from L-p2' into L-p1' is again a nuclear operator. As applications, we get the symbol of the product of the nuclear operators with bounded operators.}},
  author       = {{Kumar, Vishvesh and Mondal, Shyam Swarup}},
  issn         = {{1662-9981}},
  journal      = {{JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS}},
  keywords     = {{Pseudo-differential operators,Finite measure space,Fourier transform,S-operators,Z-operators,L-P-NUCLEARITY,PSEUDODIFFERENTIAL-OPERATORS,COMPACT,HAUSDORFF,ADJOINTS,TRACES}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{1031--1058}},
  title        = {{Nuclearity of operators related to finite measure spaces}},
  url          = {{http://doi.org/10.1007/s11868-020-00353-z}},
  volume       = {{11}},
  year         = {{2020}},
}
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