Boundary ellipticity and limiting L1-estimates on halfspaces

We identify necessary and sufficient conditions on kth order differential operators A in terms of a fixed halfspace H+⊂Rn such that the Gagliardo–Nirenberg–Sobolev inequality‖Dk−1u‖Lnn−1(H+)⩽c‖Au‖L1(H+)for u∈Cc∞(Rn,V) holds. This comes as a consequence of sharp trace theorems on H=∂H+.