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}
|
| 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:analysis
gptkb:probability_theory functional analysis |
| gptkbp:bfsParent |
gptkb:Young's_inequality
|
| gptkbp:bfsLayer |
4
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hölder's inequality
|