tags:definition |functional

Lp Norm

Context

Statements

Definition. Let $\Omega \subset {\mathbb{R}}^n$ be an open set and $p\ge 1$ a real number. Let $X=L^p(\Omega )$ be the set of all functions $f$ such that $|f{|}^p$ is Lebesgue integrable in $\Omega$. Define the Lp norm of $f$ as

$$||f|{|}_{L^p(\Omega )}={\left({\int }_{\Omega }|f{|}^p\right)}^{1/p}.$$

References

• @Sal08, pp. 311