Canonical Sobolev Projections of Weak Type (1,1)

Let $mathcal S$ be a second order smoothness in the $mathbb{R} DEGREESn$ setting. We can assume without loss of generality that the dimension $n$ has been adjusted as necessary so as to insure that $mathcal S$ is also non-degenerate. This title describes how $mathcal S$ must fit into one of three mutually exclusive cases, and in each of these cases the authors characterize, by a simple intrinsic condition, the second order smoothnesses $mathcal S$ whose canonical Sobolev projection $P_{mathcal{S}}$ is of weak type $(1,1)$ in the $mathbb{R} DEGR