Affine measures have been introduced in Harmonic Analysis to facilitate the study of Fourier Restriction problems and regularity of averages along curves and hypersurfaces (i.e. Radon transforms). In this talk we motivate and define the Affine Measures and then move on to discuss the geometric interpretation of such objects. We review a classical result of D. Oberlin relating such measures to a Hausdorff-type ambient measure and then discuss some new results in the same spirit (joint work with J. Hickman): geometric interpretations for the case of flat hypersurfaces, and geometric interpretations for a non-translation invariant case.
Affine measures in Harmonic Analysis: geometric interpretations
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Nom de l'orateur
Marco Vitturi
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LMJL
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