KnowraHölder's inequalityLinked fromLinked fromThe 21 pages that link to Hölder's inequality, each with the reason it gives.All 21Related 15Compared with 6Cauchy–Schwarz inequalityRelated: Cauchy–Schwarz is its special case with both exponents equal to two.Jensen's inequalityCompared with: It controls products through norms, rather than comparing a function of an average with an average of function values.Lp spaceRelated: It controls products of functions from paired Lp spaces.Equality conditionRelated: Its equality criterion identifies when the norm bound is attained.Chebyshev's sum inequalityCompared with: It controls product sums through magnitudes rather than matching order.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.Nesbitt's inequalityCompared with: Hölder generalizes the product-sum technique behind a Cauchy–Schwarz proof of Nesbitt.Tonelli's theoremRelated: It is a common tool for establishing integrability needed to apply Fubini's theorem.Muirhead's inequalityCompared with: Hölder handles broader product estimates, while Muirhead is specialized to symmetric monomials.Titu's lemmaCompared with: Hölder generalizes the product estimate behind Cauchy–Schwarz to exponents beyond two.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.Abel's inequalityCompared with: It offers a general product bound without Abel's partial-sum structure.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.
KnowraHölder's inequalityLinked fromLinked fromThe 21 pages that link to Hölder's inequality, each with the reason it gives.All 21Related 15Compared with 6Cauchy–Schwarz inequalityRelated: Cauchy–Schwarz is its special case with both exponents equal to two.Jensen's inequalityCompared with: It controls products through norms, rather than comparing a function of an average with an average of function values.Lp spaceRelated: It controls products of functions from paired Lp spaces.Equality conditionRelated: Its equality criterion identifies when the norm bound is attained.Chebyshev's sum inequalityCompared with: It controls product sums through magnitudes rather than matching order.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.Nesbitt's inequalityCompared with: Hölder generalizes the product-sum technique behind a Cauchy–Schwarz proof of Nesbitt.Tonelli's theoremRelated: It is a common tool for establishing integrability needed to apply Fubini's theorem.Muirhead's inequalityCompared with: Hölder handles broader product estimates, while Muirhead is specialized to symmetric monomials.Titu's lemmaCompared with: Hölder generalizes the product estimate behind Cauchy–Schwarz to exponents beyond two.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.Abel's inequalityCompared with: It offers a general product bound without Abel's partial-sum structure.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.