5.1 In this section we prove several fundamental inequalities. For example, if p, q, and r with 1/p + 1/q = 1/r belong to [0, +∞], and if f, g are two functions on Ω such that N p (f) and N q (g) are finite, then N r (fg) ≤ N p (f)N q (g) (Proposition 5.1.2). Theorem 1.1 is a generalization of Minkowski’s inequality: if f and g are two functions on Ω and p ≥ 1, then N p (f + g) ≤ N p (f) + N p (g).