2025/01/26 by Boza, Santiago, Křepela, Martin, Soria, Javier
#46B42 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2501.15565
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-\frac1p 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.