Category:Lipschitz Norm

This category contains results about Lipschitz Norm.

Let $\struct {X _\mathbf A, \sigma_\mathbf A}$ be a shift of finite type.

Let $\theta \in \openint 0 1$.

Let $\map {F_\theta} {X _\mathbf A}$ be the Lipschitz space on $X _\mathbf A$.

The Lipschitz norm on $F_\theta$ is defined as:

$\forall f \in F_\theta: \norm f_\theta := \norm f_\infty + \size f_\theta$

where:

$\norm f_\infty$ denotes the supremum norm of $f$

$\size f_\theta$ denotes the Lipschitz seminorm.