%0 Journal Article
%A Boza, Santiago
%A Křepela, Martin
%A Soria de Diego, Francisco Javier
%T Rearrangement-invariant norms commuting with dilations
%D 2026
%U https://hdl.handle.net/20.500.14352/131938
%X We study rearrangement-invariant spaces X over [0, ∞) for which there exists a function h : (0, ∞) → (0, ∞) such that ∥Drf∥X = h(r)∥f∥X for all f ∈ X and all r > 0, where Dr is the dilation operator. It is shown that this may hold only if h(r) = r− 1 p for all r > 0, in which case the norm ∥·∥X is called p-homogeneous. We investigate which types of r.i. spaces satisfy this condition and show some important embedding properties.
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