The lattice structure of negative Sobolev and extrapolation spaces

Sahiba Arora, Jochen Glück, Felix L. Schwenninger

It is well-known that the Sobolev spaces $W^{k,p}({\mathbb{R}}^d)$ are vector lattices with respect to the pointwise almost everywhere order if $k\in \{0,1\}$, but not if $k\ge 2$.…