What question did this study set out to answer?

This research aims to extend the Sobolev embedding theorem for vector-valued functions, building on its established foundation for single-valued functions.

April 1, 2026Open Access

Improved Sobolev embedding theorems for vector-valued functions

Key Points

This research aims to extend the Sobolev embedding theorem for vector-valued functions, building on its established foundation for single-valued functions.
Introduced embedding theorems specific to vector-valued functions.
Examined the relationships with massless Dirac operators.
Utilized both three-dimensional and four-dimensional Dirac operator frameworks.
Established new embedding results involving the three-dimensional massless Dirac operator.
Demonstrated applicability to both Weyl-Dirac and Cauchy-Riemann operators.
Showed compatibility of new results with existing theories in functional analysis.

Abstract

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.

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