Poincaré-Type Inequalities for Green’s Operator on Harmonic Forms



In this paper, we prove the local Poincaré-type inequalities with singular factors for Green’s operator applied to harmonic forms and extend the local results into the global cases in John domains. We also establish the local Poincaré-type inequalities with Orlicz norms for Green’s operator on harmonic forms and global inequalities in \(L^{\varphi }(m)\)-averaging or averaging domains.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsSeattle UniversityWAUSA
  2. 2.Department of MathematicsHarbin Institute of TechnologyHarbinPeople’s Republic of China

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