Statements (19)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:inequality
|
gptkbp:appliesTo |
integrals
sums |
gptkbp:category |
Inequalities
|
gptkbp:firstPublished |
1889
|
gptkbp:generalizes |
gptkb:Cauchy-Schwarz_inequality
|
gptkbp:hasDiscreteForm |
Σ|a_i b_i| ≤ (Σ|a_i|^p)^{1/p} (Σ|b_i|^q)^{1/q}
|
https://www.w3.org/2000/01/rdf-schema#label |
Hölder's inequality
|
gptkbp:namedAfter |
gptkb:Otto_Hölder
|
gptkbp:relatedTo |
gptkb:Lp_spaces
|
gptkbp:sentence |
For measurable functions f and g and conjugate exponents p, q > 1 with 1/p + 1/q = 1, ∫|fg| ≤ (∫|f|^p)^{1/p} (∫|g|^q)^{1/q}.
|
gptkbp:usedFor |
bounding integrals
establishing duality in Lp spaces proving convergence |
gptkbp:usedIn |
gptkb:probability_theory
analysis functional analysis |
gptkbp:bfsParent |
gptkb:Young's_inequality
|
gptkbp:bfsLayer |
4
|