NOTE ON LINEARITY OF REARRANGEMENT-INVARIANT SPACES

Abstract

For some rearrangement-invariant functional parallel to center dot parallel to(x) having the lattice property, we give a characterization of linearity of the set {f : parallel to f parallel to(x) < infinity}. Afterwards we apply this general abstract theorem in the case of Orlicz-Lorentz spaces.

Keywords

• rearrangement-invariant lattice
• Lorentz Orlicz spaces
• weighted inequalities
• non-increasing rearrangement
• Banach function spaces