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
A -space is a compact set with respect to a quasi-metric and a Borel measure such that the measure of a ball of radius is equivalent to , where . The paper deals with spaces of Besov type where and . Here is a bi-Lipschitzian map of the snowflaked version of for some , onto a fractal -set in some , reducing the spaces to the better known spaces .
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.