The sharp higher-order Lorentz–Poincaré and Lorentz–Sobolev inequalities in the hyperbolic spaces

Abstract

In this paper, we study the sharp Poincaré inequality and the Sobolev inequalities in the higher-order Lorentz–Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in Nguyen VH (J Math Anal Appl, 490(1):124197, 2020) to the higher-order derivatives and seem to be new in the context of the Lorentz–Sobolev spaces defined in the hyperbolic spaces.

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Correspondence to Van Hoang Nguyen.

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Nguyen, V. The sharp higher-order Lorentz–Poincaré and Lorentz–Sobolev inequalities in the hyperbolic spaces. Annali di Matematica (2021). https://doi.org/10.1007/s10231-021-01072-y

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Keywords

  • Poincaré inequality
  • Poincaré–Sobolev inequality
  • Lorentz–Sobolev space
  • Hyperbolic space

Mathematics Subject Classification

  • 26D10
  • 46E35
  • 46E30