How to measure smoothness of distributions on Riemannian symmetric manifolds and Lie group? (English) Zbl 0685.46020

Triebel, H.

Z. Anal. Anwend. 7, No. 5, 471-480 (1988).

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.

Reviewer: P.Kruszyński

MSC:

46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46F05	Topological linear spaces of test functions, distributions and ultradistributions

Keywords:

Riemannian manifolds; hyperbolic manifolds; Lie groups; scales of function spaces; Hölder-Zygmund; Besov; Sobolev; Hardy spaces; smoothness of distributions; globally symmetric manifolds; Fourier analytical tools; spectral means; convolutions