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

Abstract

The paper analyzes the decay of any zero modes that might exist for a massless Dirac operator H≔α⋅(1∕i)∇+Q, where Q is 4×4 matrix valued and of order O(∣x∣−1) at infinity. The approach is based on inversion with respect to the unit sphere in R3 and establishing embedding theorems for Dirac–Sobolev spaces of spinors f which are such that f and Hf lie in (Lp(R3))4, 1⩽p<∞.