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

Abstract

The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where $Q$ is $4\times 4$-matrix-valued and of order $O(|\x|^{-1})$ at infinity. The approach is based on inversion with respect to the unit sphere in ${\mathbb{R}}^3$ and establishing embedding theorems for Dirac-Sobolev spaces of spinors $f$ which are such that $f$ and $Hf$ lie in $(L^p({\mathbb{R}}^3){)}^4,1\le p<\infty .$

11 pages

References in corpus (2)

• The asymptotic limits of zero modes of massless Dirac operators
• The zero modes and zero resonances of massless Dirac operators