Joint BCAM-UPV/EHU Analysis and PDE seminar: Smoothing properties of averages over curves

LOCATION: UPV/EHU

Abstract
The regularity property of integral transforms is a fundamental subject in classical harmonic analysis. In this talk, we are concerned with the smoothing properties of the averaging operator defined by convolution with a measure on a smooth non-degenerate curve. Despite the simple geometric structure of the curve, the sharp smoothing estimates have remained largely unknown except for those in low dimensions until recently. We prove the sharp Sobolev regularity estimates in every dimension bigger than 4. Besides, we obtain the sharp local smoothing estimates, which consequently establish a nontrivial Lp bound on the maximal function associated with the nondegenerate curves in dimensions bigger than 3. 


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