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

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.