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.
Citazione: | 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. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Titolo: | L^p-L^p' estimates for overdetermined Radon transforms | |
Autori: | Brandolini, L; Greenleaf, A; Travaglini, G | |
Autori: | ||
Data di pubblicazione: | 2007 | |
Lingua: | English | |
Rivista: | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | |
Appare nelle tipologie: | 01 - Articolo su rivista |