Lipschitz-free spaces over products of sequences

2026/07/30 by Fraser Mason · 1 citation
Mathematics · #math.FA #msc:46B03 #msc:46E15 #msc:26A16

paper · pdf

15 pages

arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We answer positively a question of Aliaga and show that for any nonconstant real polynomial p, the Lipschitz-free space over \(p(n), p(m)):n, m∈ ℕ\ is isomorphic to F(ℤ²). We in fact show more generally that if d∈ ℕ, q∈ ℤ_{≥ 0}, and ((a_n⁽ⁱ⁾)_n=1^∞)_i=1^d, ((b_m^(j))_m=1^∞)_j=1^q are sequences with 0<a₁⁽ⁱ⁾<a₂⁽ⁱ⁾<⋯, 0<b₁^(j)<b₂^(j)<⋯, a_n⁽ⁱ⁾→ ∞ as n→ ∞, \fraca_n+1⁽ⁱ⁾a_n⁽ⁱ⁾→ 1 as n→ ∞ and \undersetm→ ∞\liminf\fracb_m+1^(j)b_m^(j)>1 for all i, j, then the Lipschitz-free space over the product of these d+q sequences is isomorphic to F(ℤ^d).

Citations

• Lipschitz spaces over non-porous sets
• On curve-flat Lipschitz functions and their linearizations
• Some remarks on the structure of Lipschitz-free spaces
• Products of Lipschitz-free spaces and applications
• The non-linear geometry of Banach spaces after Nigel Kalton
• Approximation properties and Schauder decompositions in Lipschitz-free spaces
• Planar Earthmover is not in L₁

Cited by

• Lipschitz-free spaces over non-porous subsets of ℝⁿ

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