N. J. Kalton, G. Lancien
Published 2007-08-29Version 1
We answer a question of Aharoni by showing that every separable metric space can be Lipschitz 2-embedded into $c_0$ and this result is sharp; this improves earlier estimates of Aharoni, Assouad and Pelant. We use our methods to examine the best constant for Lipschitz embeddings of the classical $\ell_p-$spaces into $c_0$ and give other applications. We prove that if a Banach space embeds almost isometrically into $c_0$, then it embeds linearly almost isometrically into $c_0$. We also study Lipschitz embeddings into $c_0^+$.
Lipschitz Embeddings of Metric Spaces into $c_0$
On the best constant in {G}affney inequality
The best constant in the embedding of $W^{N,1}({\mathbb R}^N)$ into $L^\infty({\mathbb R}^N)$
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