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Функциональный анализ и его приложения
23 февраля 2023 г. 08:30–09:30, г. Ташкент, Онлайн на платформе Zoom
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On the sharp estimates for convolution operators with oscillatory kernel
I. A. Ikromov Samarkand Regional Branch of the Institute of Mathematics named after V.I. Romanovsky, Uzbekistan Academy of Sciences
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Эта страница: | 74 |
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Аннотация:
In this talk, we the consider the $L^p\mapsto L^{p'}$-boundedness problem for convolution operators $M_k$ with oscillatory kernel. We study the convolution operators assuming that $S$ is contained in a sufficiently small neighborhood of a given point $x^0\in S$ at which exactly one of the principal curvatures of $S$ does not vanish. Such surfaces exhibit singularities of type $A$ in the sense of Arnold’s classification. Denoting by $k_p$ the minimal exponent such that $M_k$ is $L^p\mapsto L^{p'}$-bounded for $k>k_p,$ we show that the number $k_p$ depends on some discrete characteristics of the surface given as the graph of function having singularities of type $A$.
Website:
https://us02web.zoom.us/j/8022228888?pwd=b3M4cFJxUHFnZnpuU3kyWW8vNzg0QT09
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