Improved Sobolev embedding theorems for vector-valued functions

The aim of this paper is to give an extension of the improved Sobolev embedding theorem for single-valued functions to the case of vector-valued functions which is involved with the three-dimensional massless Dirac operator together with the three- or two-dimensional Weyl-Dirac (or Pauli) operator, the Cauchy-Riemann operator and also the four-dimensional Euclidian Dirac operator.