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VIDEO LIBRARY |
Conference on the Theory of Functions of Several Real Variables, dedicated to the 90th anniversary of O. V. Besov
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Multilinear pseudo-differential operators on the multidimensional torus D. B. Bazarkhanov Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty |
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Abstract: In the talk, we discuss some results on the boundedness of the toroidal linear pseudo-differential operators of the form $$ T_\sigma (f; x) := \sum_{\xi\in\mathbb{Z}^m} \sigma(x, \xi) \widehat{f}(\xi) e^{2\pi i \xi x} $$ and multilinear pseudo-differential operators of the form $$ T_\sigma (f_1, \ldots, f_n; x) := \sum_{(\xi_1, \ldots, \xi_n)\in\mathbb{Z}^{nm}} \sigma(x, \xi_1, \ldots, \xi_n) \widehat{f}_1(\xi_1)\times \cdots \times\widehat{f}_n(\xi_n) e^{2\pi i (\xi_1 + \cdots + \xi_n) x} $$ with the symbols from the Hörmander class and from its multilinear analog, respectively, as operators from the Nikol'skii–Besov or Lizorkin–Triebel function spaces and from the tensor product of such spaces into other similar spaces. |