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 ${\mathbb{R}}^3$ to clarify its relationship with the corresponding Sobolev spaces. It is shown that for $1<p<\infty$, they coincide, while for $p=1$, the latter spaces are proper subspaces of the former.

to appear in Funkcialaj Ekvacioj, 2010

References in corpus (1)

• Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators