 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/ii/paper-2/23j/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

1/ p + 1/ q = 1

f \in L^{p}

and

g \in L^{q}

imply

f g \in L^{1}

and

\int ∣ f g ∣ d μ \leq ∥ f ∥_{p} ∥ g ∥_{q} .

It includes

p = 1, q = \infty

(and the reversed case), with the essential-supremum norm for

L^{\infty}

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