Let $0 \lt p q\leq \infty $ and $\alpha \in (0,\infty ]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha ),L_q(0,\alpha ))$ in terms two monotonicity properties, extending known results which mainly de

We introduce the concept of weak k-majorization extending the classical notion of weak sub-majorization. For integers k and n with k n a vector x 2 R is weakly k-majorized by a vector q 2 R if the sum of the r largest components of x does not exceed the sum of the r largest components of q, for r = 1; : : : ; k. For a given q the set of vectors weakly k-majorized by q de nes a polyhedron P (q;k...