  This paper establishes $L^p$-improving estimates for a variety of Radon-like
transforms which integrate functions over submanifolds of intermediate
dimension. In each case, the results rely on a unique notion of curvature which
relates to, but is distinct from, Phong-Stein rotational curvature. The results
obtained are sharp up to the loss of endpoints. The methods used are a new
adaptation of the familiar method of inflation developed by Christ and others.
Unlike most previous instances of this method, the present application does not
require any particular linear algebraic relations to hold for the dimension and
codimension.
