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Factorisation of Lipschitz functions on zero dimensional groups
Published online by Cambridge University Press: 17 April 2009
Abstract
Let G denote a locally compact metrisable zero dimensional group with left translation invariant metric d. The Lipschitz spaces are defined by
where af: x → f(ax) and α > 0; when r = ∞ the members of Lip(α; r) are taken to be continuous. For a suitable choice of metric it is shown that , where 1 ≤ p ≤ 2, α > q−1, p, q are conjugate indices and . It is also shown that for G infinite the range of values of α cannot be extended.
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- Copyright © Australian Mathematical Society 1981
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