Uniform homeomorphisms between the unit balls in 𝐿_{𝑝} and 𝑙_{𝑝}

Lövblom, Gun-Marie

doi:10.1090/S0002-9939-1995-1227523-8

Uniform homeomorphisms between the unit balls in $L_ p$ and $l_ p$
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Proc. Amer. Math. Soc. 123 (1995), 405-409 Request permission

Abstract:

Let $T:B({L_p}) \to B({l_p}),1 \leq p < 2$, be a uniform homeomorphism with modulus of continuity ${\delta _T}$. It is shown that for any $\gamma ,0 \leq \gamma < \frac {{2 - p}}{{2p}}$, there exists $K > 0$ and a sequence $\{ {\varepsilon _n}\}$ with ${\varepsilon _n} \to 0$ such that $\delta _T^{ - 1}({\delta _T}({\varepsilon _n})) \geq K{\varepsilon _n}|\log {\varepsilon _n}{|^\gamma }$ for all ${\varepsilon _n}$.

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Une remarque sur l’homéomorphie des champs fonctionnels

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