Journal of Inequalities and Applications
Volume 2 (1998), Issue 3, Pages 195-228
doi:10.1155/S1025583498000125
Abstract
Sobolev inequalities in two-dimensional hyperbolic space ℍ2 are dealt with. Here ℍ2 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.