RT Journal Article
T1 Rearrangement-invariant norms commuting with dilations
A1 Boza, Santiago
A1 Křepela, Martin
A1 Soria de Diego, Francisco Javier
AB 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.
PB Elsevier
YR 2026
FD 2026
LK https://hdl.handle.net/20.500.14352/131938
UL https://hdl.handle.net/20.500.14352/131938
LA eng
NO Ministerio de Ciencia e Innovación
NO Generalitat de Catalunya
NO Universidad Complutense de Madrid
NO Czech Science Foundation
DS Docta Complutense
RD 25 feb 2026