Full paper in PDF:
$% H. Triebel, A New Approach to Function Spaces on Quasi-Metric Spaces, Rev. Mat. Complut. 18 (2005), no. 1, 7–48.%$

A New Approach to Function Spaces on Quasi-Metric Spaces

Hans TRIEBEL
Mathematisches Institut
Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena
D-07740 Jena — Germany
triebel@minet.uni-jena.de

Received: November 16, 2004
Accepted: December 20, 2004
ABSTRACT

A d -space X = (X,r,m) is a compact set X with respect to a quasi-metric r and a Borel measure m such that the measure of a ball of radius r is equivalent to d r , where d > 0 . The paper deals with spaces s Bp(X;H) of Besov type where 1 < p< oo and s (- R . Here H is a bi-Lipschitzian map of the snowflaked version e (X,r,m) of X for some 0< e <1 , onto a fractal d/e -set G = HX in some n R , reducing the spaces s Bp(X;H) to the better known spaces s/e Bp (G) .

Key words: quasi-metric spaces, snowflaked transform, Besov spaces, atomic and subatomic decompositions, entropy numbers, Riesz potentials.
2000 Mathematics Subject Classification: 46E35, 28A80, 47B06, 43A85.