Conductor Inequalities and Criteria for Sobolev-Lorentz Two-Weight Inequalities

  • Serban Costea
  • Vladimir Maz'ya
Part of the International Mathematical Series book series (IMAT, volume 9)


We present integral conductor inequalities connecting the Lorentz p, q-(quasi)norm of a gradient of a function to a one-dimensional integral of the p, q-capacitance of the conductor between two level surfaces of the same function. These inequalities generalize an inequality obtained by the second author in the case of the Sobolev norm. Such conductor inequalities lead to necessary and sufficient conditions for Sobolev-Lorentz type inequalities involving two arbitrary measures.


Dirichlet Form Lorentz Space Nonlinear Elliptic Equation Sobolev Type Potential Anal 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.McMaster UniversityHamiltonCanada
  2. 2.Ohio State UniversityColumbusUSA

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