On the Fréchet space Lp_

[EN] This paper contains a study of the structure of the Frechet space L-p- , 1 < P less than or equal to infinity, defined as the intersection of Lq[0, 1] for q < p, and endowed with the projective topology. The main topics covered are: normable, Schwartz and nuclear subspaces of L-p-;construction of uncomplemented copies of l(2) inside L-p- for p < 2; construction of Montel non-Schwartz subspaces; the space L-p- is primary.