Hyperbolic Q p -scales

The Q p -scales were first introduced in [1] as interpolation spaces be-tween the Bloch and Dirichlet spaces in the complex space. In ’98, they were generalized to IR n (see [4], [6]) using the automorphisms of the unit disk ϕ a ( x ) = x − a 1 − ax , | a | < 1 , and a modified fundamental solution for the Laplacian. However, such treatment presents the disadvantage of only consider-ing the Euclidean case. In order to obtain an approach to homogeneous hyperbolic manifolds, the projective model of Gel’fand was retaken in [2]. With the help of a convenient fundamental solution for the hyperbolic (homogeneous of degree α ) D α (see [5]) it was introduced in [7] and [3] equivalent Q p scales for homogeneous hyperbolic spaces. In this talk we shall present and study some properties of this hyperbolic scale.