@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://doi.org/10.1007/s00041-019-09689-7}},
  volume       = {{25}},
  year         = {{2019}},
}

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