We prove several variations on the results in Ricci and Travaglini [Convex curves, Radon transforms and convolution operators defined by singular measures, [Proc. Amer. Math. Soc. v.129 (2001) pp. 1739-1744] concerning L^p-L^{p'} bounds for convolution with all rotations of a measure supported by a fixed convex curve in R^2. Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth k-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare the approach of Ricci and Travaglini, based on average decay of the Fourier transform, with an approach based on L^2 boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using different techniques.

Brandolini, L., Greenleaf, A., & Travaglini, G. (2007). L^p-L^p' estimates for overdetermined Radon transforms. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359, 2559-2575.

L^p-L^p' estimates for overdetermined Radon transforms

TRAVAGLINI, GIANCARLO
2007

Abstract

We prove several variations on the results in Ricci and Travaglini [Convex curves, Radon transforms and convolution operators defined by singular measures, [Proc. Amer. Math. Soc. v.129 (2001) pp. 1739-1744] concerning L^p-L^{p'} bounds for convolution with all rotations of a measure supported by a fixed convex curve in R^2. Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth k-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare the approach of Ricci and Travaglini, based on average decay of the Fourier transform, with an approach based on L^2 boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using different techniques.
Articolo in rivista - Articolo scientifico
Radon transform; convolution operators
English
2559
2575
Brandolini, L., Greenleaf, A., & Travaglini, G. (2007). L^p-L^p' estimates for overdetermined Radon transforms. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 359, 2559-2575.
Brandolini, L; Greenleaf, A; Travaglini, G
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/6073
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