Семинары: И. А. Икромов, On the sharp estimates for convolution operators with oscillatory kernel

СЕМИНАРЫ


Функциональный анализ и его приложения 23 февраля 2023 г. 08:30, г. Ташкент, Онлайн на платформе Zoom

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
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