A CONSTRUCTIVE PROOF OF THE ASSOUAD EMBEDDING THEOREM WITH BOUNDS ON THE DIMENSION

Guy David (1) , Marie Snipes (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 mathematics

We give a constructive proof of a theorem of Naor and Neiman, (to appear, Revista Matematica Iberoamercana), which asserts that if $(E,d)$ is a doubling metric space, there is an integer $N > 0$, that depends only on the metric doubling constant, such that for each exponent $\alpha \in (1/2,1)$, we can find a bilipschitz mapping $F = (E,d^{\alpha}) \to \R^N$.

Mots clés: Assouad Embedding; doubling metric spaces; snowflake distance

Domaines: Analyse classique [math.CA]

Guy David, Marie Snipes. A CONSTRUCTIVE PROOF OF THE ASSOUAD EMBEDDING THEOREM WITH BOUNDS ON THE DIMENSION. 2012. ⟨hal-00751548⟩