Hölder's inequality

GPTKB entity

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