Equivalent Norms on Lipschitz Space/Shift of Finite Type
Jump to navigation
Jump to search
Theorem
Let $\struct {X, \sigma}$ be a shift of finite type.
Let $F_\theta$ be the Lipschitz space on $X$.
Let $x_0 \in F_\theta$.
Then the following norms on $F_\theta$ are equivalent:
- $(1): \quad$ Lipschitz norm $\norm\cdot_\theta$
- $(2): \quad \forall f \in F_\theta : \norm f '_\theta := \cmod {\map f {x_0} } + \size f_\theta$
Proof
This theorem requires a proof. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |