The MathNet Korea
Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

한국고등과학원 세미나
Title Sharp estimates for singular multiplier operators on Lebesgue spaces
Date 2018-12-19
Speaker Kwon, Yehyun(SNU)
Sponsors 2018-12-19
Host KIAS
Place 1423
Abstract By the Fourier inversion numerous operators appearing in mathematical analysis, partial differential equations, and mathematical physics are represented as Fourier multiplier operators. In most cases the associated multipliers have their singularities on certain submanifolds, and regularity properties of such operators are naturally related to the singularities of the multipliers. I will talk about several singular multiplier operators which play important roles in mathematical analysis, and aim to completely characterize mapping properties of these operators on Lebesgue spaces. Those include sharp estimates for the spherical harmonic projections, sharp resolvent estimates for the Laplacian, and Carleman estimates for second order differential operators. I will also give some applications of the estimates to partial differential equations and spectral theory. This talk is based on recent joint works with Eunhee Jeong and Sanghyuk Lee.