Improved Sobolev Embedding Theorems for Vector-Valued Functions

Takashi Ichinose; Yoshimi Saitō

doi:10.1619/fesi.57.245

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Keywords: Sobolev inequality, Gagliardo-Nirenberg inequality, Improved Sobolev embedding theorem, Dirac-Sobolev inequality, Sobolev inequality for vector-valued functions, Dirac operator

JOURNAL FREE ACCESS

2014 Volume 57 Issue 2 Pages 245-295

DOI https://doi.org/10.1619/fesi.57.245

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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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