Estimates for Overdetermined Radon Transforms
نویسندگان
چکیده
We prove several variations on the results in Ricci and Travaglini[RT] concerning L−L ′ bounds for convolution with all rotations of a measure supported by a fixed convex curve in R. Estimates are obtained for averages over higherdimensional convex (nonsmooth) hypersurfaces, smooth k-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare the approach of [RT], based on average decay of the Fourier transform, with an approach based on L boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using different techniques. §
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