RELATION BETWEEN THE SPACE $M_{\Psi}$ AND WEAK $L_P$

We showed the upper p-estimate and p-power concavity are the necessary and sufficient condition of the space $M_{\Psi}$to be weak $L_pX>.

Soviet Math. Dokl. v.5 Imbedding theorem for Banach Spaces of measurable function E.M.Semenov
J. Functional Anlysis v.11 Spaces $A_α$(X) and interpolation R.Sharpley
p-power quasi-concavity of a r. i.space Chongsung Lee
Function spaces, Ergeb. der Math. U. ihr. Grenzgeb 97 Classical Banach spaces Ⅱ J.Lindenstrauss;L.Tazfriri
English transl. Transl. Math. Mono v.54 Interpolation of linear operators S.Krein;J.Petunim;E.Semenov
Acta. Math. A cad. Sci. Hunger v.21 Concave majority of positive functions J.Peetree