How to measure smoothness of distributions on Riemannian symmetric manifolds and Lie group?
The author considers some types of Riemannian manifolds, hyperbolic manifolds and Lie groups, and function spaces connected with them. In particular, he introduces two scales of function spaces on them which cover such classical function spaces as the Hölder-Zygmund, Besov, Sobolev, and Hardy spaces. The smoothness of distributions is measured via introduced means over the above mentioned structures. The considerations are restricted to the case of globally symmetric manifolds to allow the use of Fourier analytical tools, spectral means and convolutions.
scientific article; zbMATH DE number 4122614