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Two-Weighted Intergal Inequalities for Differential Forms

  • Xiuyin, Shang (College of Science, Agricultural University of Hebei) ;
  • Zhihua, Gu (College of Science, Agricultural University of Hebei) ;
  • Zengbo, Zhang (College of Science, Agricultural University of Hebei)
  • Received : 2006.01.06
  • Accepted : 2008.05.14
  • Published : 2009.09.30

Abstract

In this paper, we make use of the weight to obtain some two-weight integral inequalities which are generalizations of the Poincar$\'{e}$ inequality. These inequalities are extensions of classical results and can be used to study the integrability of differential forms and to estimate the integrals of differential forms. Finally, we give some applications of this results to quasiregular mappings.

Keywords

differential form;Poincar$\'{e}$ inequality;A-harmonic equation;H$\"{o}$lder inequality

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