Abstract

CARDONA, Duván  and  KUMAR, Vishvesh. Multilinear analysis for discrete and periodic pseudo-differential operators in L^p-spaces. Integración - UIS [online]. 2018, vol.36, n.2, pp.151-164. ISSN 0120-419X.  https://doi.org/10.18273/revint.v36n2-2018006.

In this note we announce our investigation on the L p properties for periodic and discrete multilinear pseudo-differential operators. First, we review the periodic analysis of multilinear pseudo-differential operators by showing classical multilinear Fourier multipliers theorems (proved by Coifman and Meyer, Tomita, Miyachi, Fujita, Grafakos, 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. The s-nuclearity, 0 < s ≤ 1, for the discrete and periodic multilinear pseudo-differential operators will be investigated. To do so, we classify those s-nuclear, 0 < s ≤ 1, multilinear integral operators on arbitrary Lebesgue spaces defined on σ-finite measures spaces. Finally, we present some applications of our analysis 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.

MSC2010: 58J40, 47B10, 47G30, 35S30.

Keywords : Pseudo-differential operator; discrete operator; periodic operator; nuclearity; boundedness; Fourier integral operator; multilinear analysis.

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