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Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on ℤⁿ and the torus 𝕋ⁿ

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Abstract
In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on L-p-spaces. First, we prove analogues of known multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Grafakos, Tomita, Torres, Kenig, Stein, Fujita, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. Later, we investigate the s-nuclearity, 0 < s <= 1, of periodic and discrete pseudo-differential operators. To accomplish this, we classify those s-nuclear multilinear integral operators on arbitrary Lebesgue spaces defined on sigma-finite measures spaces. We also study similar properties for periodic Fourier integral operators. Finally, we present some applications of our study to deduce the periodic Kato-Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.
Keywords
Multilinear pseudo-differential operator, Discrete operator, Periodic operator, Nuclearity, Boundedness, Fourier integral operators, Multilinear analysis, APPROXIMATION PROPERTY, FOURIER MULTIPLIERS, SCHATTEN CLASSES, TRACE FORMULA, MIXED-NORM, COMPACT, ADJOINTS, THEOREM

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MLA
Cardona Sanchez, Duvan, and Vishvesh Kumar. “Lp-Boundedness and Lp-Nuclearity of Multilinear Pseudo-Differential Operators on ℤn and the Torus 𝕋n.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, 2019, pp. 2973–3017, doi:10.1007/s00041-019-09689-7.
APA
Cardona Sanchez, D., & Kumar, V. (2019). Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on ℤn and the torus 𝕋n. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25, 2973–3017. https://doi.org/10.1007/s00041-019-09689-7
Chicago author-date
Cardona Sanchez, Duvan, and Vishvesh Kumar. 2019. “Lp-Boundedness and Lp-Nuclearity of Multilinear Pseudo-Differential Operators on ℤn and the Torus 𝕋n.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25: 2973–3017. https://doi.org/10.1007/s00041-019-09689-7.
Chicago author-date (all authors)
Cardona Sanchez, Duvan, and Vishvesh Kumar. 2019. “Lp-Boundedness and Lp-Nuclearity of Multilinear Pseudo-Differential Operators on ℤn and the Torus 𝕋n.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25: 2973–3017. doi:10.1007/s00041-019-09689-7.
Vancouver
1.
Cardona Sanchez D, Kumar V. Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on ℤn and the torus 𝕋n. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2019;25:2973–3017.
IEEE
[1]
D. Cardona Sanchez and V. Kumar, “Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on ℤn and the torus 𝕋n,” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, pp. 2973–3017, 2019.
@article{8623028,
  abstract     = {{In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on L-p-spaces. First, we prove analogues of known multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Grafakos, Tomita, Torres, Kenig, Stein, Fujita, Tao, etc.) in the context of periodic and discrete multilinear pseudo-differential operators. For this, we use the periodic analysis of pseudo-differential operators developed by Ruzhansky and Turunen. Later, we investigate the s-nuclearity, 0 < s <= 1, of periodic and discrete pseudo-differential operators. To accomplish this, we classify those s-nuclear multilinear integral operators on arbitrary Lebesgue spaces defined on sigma-finite measures spaces. We also study similar properties for periodic Fourier integral operators. Finally, we present some applications of our study to deduce the periodic Kato-Ponce inequality and to examine the s-nuclearity of multilinear Bessel potentials as well as the s-nuclearity of periodic Fourier integral operators admitting suitable types of singularities.}},
  author       = {{Cardona Sanchez, Duvan and Kumar, Vishvesh}},
  issn         = {{1069-5869}},
  journal      = {{JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS}},
  keywords     = {{Multilinear pseudo-differential operator,Discrete operator,Periodic operator,Nuclearity,Boundedness,Fourier integral operators,Multilinear analysis,APPROXIMATION PROPERTY,FOURIER MULTIPLIERS,SCHATTEN CLASSES,TRACE FORMULA,MIXED-NORM,COMPACT,ADJOINTS,THEOREM}},
  language     = {{eng}},
  pages        = {{2973--3017}},
  title        = {{Lp-boundedness and Lp-nuclearity of multilinear pseudo-differential operators on ℤⁿ and the torus 𝕋ⁿ}},
  url          = {{http://dx.doi.org/10.1007/s00041-019-09689-7}},
  volume       = {{25}},
  year         = {{2019}},
}

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