The Schwartz space \(\mathcal{S}(\mathbb{R}^n)\) is a dense subspace of \(L^p(\mathbb{R}^n)\) for every \(p\in [1,\infty )\).
Remarks
- The statement is not true for \(p=\infty\).
The Schwartz space \(\mathcal{S}(\mathbb{R}^n)\) is a dense subspace of \(L^p(\mathbb{R}^n)\) for every \(p\in [1,\infty )\).