The sharp higher order Lorentz--Poincar\'e and Lorentz--Sobolev inequalities in the hyperbolic spaces
Abstract
In this paper, we study the sharp Poincar\'e inequality and the Sobolev inequalities in the higher order Lorentz--Sobolev spaces in the hyperbolic spaces. These results generalize the ones obtained in Nguyen2020a 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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