Resumen de Boundary spaces for inclusion map between rearrangement invariant spaces

S. Ya. Novikov

• Let $E([0, 1];m)$ be a rearrangement invariant space (\texttt{RIS}) on [0, 1] with Lebesgue measure $m$. That is, $E$ is a Banach lattice and if $m(t: \vert x(t)\vert > \tau) = m(t: \vert y(t)\vert >\tau)\forall\tau$ , then $\parallel x\parallel_E = \parallel y\parallel_E$. For each of this kind of spaces we have inclusions $C\subset L_\infty\subset E\subset L_1$ and canonical inclusion maps $I(C,E)$ or $I(E_1,E_2)$. The aim of this paper is to represent a number of \texttt{RIS}, which are boundary for various properties of canonical inclusion maps. There are still some unsolved problem in this area.