Journal of Inequalities and Applications
Volume 2 (1998), Issue 3, Pages 195-228

Sobolev inequalities in 2-D hyperbolic space: A borderline case

Francesco Mugelli and Giorgio Talenti

Dipartimento di Matematica dell'Università, Viale Morgagni 67A, Firenze 1-50134, Italy

Received 30 March 1997

Copyright © 1998 Francesco Mugelli and Giorgio Talenti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Sobolev inequalities in two-dimensional hyperbolic space 2 are dealt with. Here 2 is modeled on the upper Euclidean. half-plane equipped with the Poincaré–Bergman metric. Some borderline inequalities, where the leading exponent equals the dimension, are focused. The technique involves rearrangements of functions, and tools from calculus of variations and ordinary differential equations.