Dirac–Sobolev Spaces and Sobolev Spaces

Abstract

The aim of this work is to study the first order Dirac-Sobolev spaces in L^p norm on an open subset of R³ to clarify its relationship with the corresponding Sobolev spaces. It is shown that for 1 < p < ∞, they coincide, while for p = 1, the latter spaces are proper subspaces of the former.