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Radon-like operators of intermediate dimension

Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017

May 15, 2017 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Philip Gressman (University of Pennsylvania)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Radon-like operators

  • harmonic analysis

  • intermediate dimension

  • Radon transform

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Gressman

Abstract

We will discuss recent results establishing $L^p$-improving estimates for Radon-like operators which average functions over submanifolds of intermediate dimension (e.g., neither curves nor hypersurfaces). The methods are built around an $L^p$-adapted $TT^*T$ argument which is itself an instance of a Christ-type method of refinements. The resulting estimates are sharp up to loss of the endpoints and provide new insights into the vector field formulation of sharp curvature conditions

Supplements
28685?type=thumb Gressman Notes 237 KB application/pdf Download
Video/Audio Files

Gressman

H.264 Video 4-Gressman.mp4 151 MB video/mp4 rtsp://videos.msri.org/data/000/028/440/original/4-Gressman.mp4 Download
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