 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/ib/paper-3/12e/b/i/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

Since

1 \leq t \leq b

and

c \geq 0

b^{- c} \leq t^{- c} \leq 1.

Taking suprema gives

b^{- c} ∥ f ∥_{\infty} \leq ∥ f ∥_{c} \leq ∥ f ∥_{\infty} .

Thus the weighted norm and the usual uniform norm are equivalent norms.

 New to topics? Read the docs here!