# Relationship between lp norms

### Rini Indrati : Two-Norm Convergence in the Lp Spaces

For n=2 it is easily proven (see below), but not for n>2. So my question is: How can relation (3) be proven for arbitrary n? Can this be generalized into something . Yes. This is a known inequality, called e.g. "Gagliardo-Nirenberg inequality" in Brezis' book, Comment 1 to Chapter 8, page Lp-norms. Let (E, E,µ) be a measure space. For 1 ≤ p Lp = Lp(E, E,µ) the set of measurable functions f with finite Lp-norm: fp = (∫E |f|pdµ).

Но тот молчал.

Конец лета. Солнце уже зашло.

Над головой автоматически зажглись лампы дневного света. Сьюзан нервничала: прошло уже слишком много времени.