Linked from

The 21 pages that link to Hölder's inequality, each with the reason it gives.

• Cauchy–Schwarz inequalityRelated: Cauchy–Schwarz is its special case with both exponents equal to two.

• Lp spaceRelated: It controls products of functions from paired Lp spaces.

• Equality conditionRelated: Its equality criterion identifies when the norm bound is attained.

• Minkowski inequalityRelated: Applying Hölder’s inequality to the expanded norm yields the Minkowski bound.

• Banach–Alaoglu theoremRelated: It confines each coordinate value of a dual unit-ball element to a compact disk.

• Rearrangement inequalityRelated: It generalizes product-sum bounds to exponents beyond the rearrangement setting.

• AM–GM inequalityRelated: Hölder generalizes product-sum bounds beyond AM–GM's equal-weight mean comparison.

• Integrable functionRelated: It shows products of suitably integrable functions remain integrable.

• Bernoulli's inequalityRelated: It is a central power-based estimate in analysis, with a different role from Bernoulli's pointwise bound.

• Tonelli's theoremRelated: It is a common tool for establishing integrability needed to apply Fubini's theorem.

• Young's inequality for productsRelated: Applying the scalar bound term by term yields the finite-sum form of Hölder's inequality.

• Bohr–Mollerup theoremRelated: Applied to the Euler integral, it shows that the gamma function is log-convex.

• Doob's martingale inequalityRelated: The moment form uses Hölder's inequality to relate the maximum's norm to the terminal value's norm.

• Agmon's inequalityRelated: It underlies many estimates that combine integrable derivatives into norm bounds.

• Carleman's inequalityRelated: Hölder's inequality gives a direct finite-sum proof and exposes the role of the constant e.