We prove several variations on the results of F. Ricci and G. Travaglini (2001), concerning
L
p
−
L
p
′
L^{p}-L^{p’}
bounds for convolution with all rotations of arc length measure on a fixed convex curve in
R
2
\mathbb {R} ^{2}
. Estimates are obtained for averages over higher-dimensional convex (nonsmooth) hypersurfaces, smooth
k
k
-dimensional surfaces, and nontranslation-invariant families of surfaces. We compare Ricci and Travaglini’s approach, based on average decay of the Fourier transform, with an approach based on
L
2
L^{2}
boundedness of Fourier integral operators, and show that essentially the same geometric condition arises in proofs using the two techniques.