EVERY REARRANGEMENT-INVARIANT QUASI-BANACH FUNCTION SPACE IS AN INTERPOLATION SPACE BETWEEN TWO LORENTZ SPACES

Source abstract

Abstract We extend some results of Kwok-Pun Ho. In particular, it will be shown that every rearrangement-invariant quasi-Banach function space on a totally $$\varvec{\sigma }$$ σ -finite measure space $$\varvec{(\Omega ,\mu )}$$ ( Ω , μ ) with a non-atomic measure $$\varvec{\mu }$$ μ can be expressed in the form $$ \varvec{E =\mathcal {F}(L_{p_0,q_0},L_{p_1,q_1})} $$ E = F ( L p 0 , q 0 , L p 1 , q 1 ) for an interpolation functor $$\varvec{\mathcal {F}}$$ F , where the construction of the functor $$\varvec{\mathcal {F}}$$ F is given based on the space E itself.