On local smoothing of Fourier integral operators
Dr. Ramesh Manna,Harish-Chandra Research Institute, Allahabad
| Speaker |
Dr. Ramesh Manna,Harish-Chandra Research Institute, Allahabad
|
|---|---|
| When |
Jun 19, 2017
from 04:00 PM to 05:00 PM |
| Where | LH 006 |
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Abstract: In this talk, we prove the local smoothing estimate for Fourier integral operators with phase function \(h(x, t, \xi)= x . \xi + t|\xi|,\) and amplitude function \(a(x,t, \xi)\) belongs to \(S^m\), the symbol class of
order m less or equal to 0. Such Fourier integral operators arise in wave equation and also in the study of spherical maximal operators. As an application of the local smoothing estimate, we give an alternative proof
of the \(L^p-\) boundedness of Bourgain's circular maximal operator on \(L^p\) \((R^2)\) for \(p>2\).