Brezis–Gallouët inequality

The Brezis–Gallouët inequality is an important result in functional analysis and partial differential equations, particularly in the context of Sobolev spaces. It provides a bound for a certain type of functional involving the fractional Sobolev norms. Specifically, the inequality can be stated as follows: Let \( n \geq 1 \) and \( p \in (1, n) \).