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# On local smoothing of Fourier integral operators

Dr. Ramesh Manna,Harish-Chandra Research Institute, Allahabad
 Speaker Dr. Ramesh Manna,Harish-Chandra Research Institute, Allahabad Jun 19, 2017 from 04:00 PM to 05:00 PM LH 006 vCal iCal

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 $$p>2$$.

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