  This paper establishes endpoint $L^p-L^q$ and Sobolev mapping properties of
Radon-like operators which satisfy a homogeneity condition (similar to
semiquasihomogeneity) and a condition on the rank of a matrix related to
rotational curvature. For highly degenerate operators, the rank condition is
generically satisfied for algebraic reasons, similar to an observation of
Greenleaf, Pramanik, and Tang concerning oscillatory integral operators.
