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Harmonic Analysis

Generalized Radon transforms, optimal Lp improving properties

speaker: Philip Gressman (Princeton University)

abstract: In this talk I will present recent work on obtaining boundary L^p-L^q estimates for Radon-like operators in various special cases. The methods are baised on work by M. Christ (IMRN, 1998), and are extended to deal with degenerate families of translation-invariant curves as well as non-degenerate families of variable curves in low dimensions (n=3,4). In the case of variable curves, the connections to left- and right-torsion are discussed, as well as new types of torsion which arise as the dimension increases. In particular, it will be demonstrated that the translation-invariant family of curves in 4 dimensions given by (t,t2,t3,t4) is, possibly contrary to expectations, degenerate.

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