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On the full range of Zippin and inclusion indices of rearrangement-invariant spaces
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Orientador(es)
Resumo(s)
Let X be a rearrangement-invariant space on [0, 1]. It is known that its Zippin indices β̲X,β¯X and its inclusion indices γX,δX are related as follows: 0≤β̲X≤1/γX≤1/δX≤β¯X≤1. We show that given β̲,β¯∈[0,1] and γ,δ∈[1,∞] satisfying β̲≤1/γ≤1/δ≤β¯, there exists a rearrangement-invariant space X such that β̲X=β̲, β¯X=β¯ and γX=γ, δX=δ.
Descrição
Funding Information:
Open access funding provided by FCT|FCCN (b-on).
Publisher Copyright:
© The Author(s) 2024.
Palavras-chave
46E30 Embedding Inclusion indices Lorentz spaces Rearrangement-invariant Banach function space Zippin indices Analysis Algebra and Number Theory Geometry and Topology Computational Mathematics Applied Mathematics