Khinchin–Kahane type inequalities

E87730

functional analysis result moment inequality norm inequality probability inequality

Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.

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Observed surface forms (3)

Surface form	Occurrences
Kahane inequality	1
Khinchin inequality	1
noncommutative Khinchin–Kahane inequalities	1

Statements (47)

Predicate	Object
instanceOf	functional analysis result ⓘ moment inequality ⓘ norm inequality ⓘ probability inequality ⓘ
appliesTo	Gaussian series ⓘ Rademacher series ⓘ series with independent symmetric coefficients ⓘ
assumes	independence of random signs or coefficients ⓘ symmetry of random signs in classical form ⓘ
field	Banach space theory ⓘ functional analysis ⓘ probability theory ⓘ random processes ⓘ
generalizes	Khinchin–Kahane type inequalities self-linksurface differs ⓘ surface form: Kahane inequality Khinchin–Kahane type inequalities self-linksurface differs ⓘ surface form: Khinchin inequality
hasProperty	constants depend on p but not on number of terms ⓘ dimension-free constants in many formulations ⓘ
hasVariant	Khinchin–Kahane type inequalities self-linksurface differs ⓘ surface form: noncommutative Khinchin–Kahane inequalities subgaussian Khinchin–Kahane inequalities ⓘ vector-valued Khinchin–Kahane inequalities ⓘ
implies	stability of random series under change of p-norm ⓘ
namedAfter	Aleksandr Khinchin NERFINISHED ⓘ Jean-Pierre Kahane ⓘ
provides	bounds between different moments ⓘ bounds between different norms ⓘ
relatedTo	Littlewood–Paley theory ⓘ cotype of a Banach space ⓘ type of a Banach space ⓘ unconditional convergence of random series ⓘ vector-valued Khinchin inequalities ⓘ
relates	L2 norm and Lp norms ⓘ Lp norms of random series ⓘ moments of random series ⓘ
typicalForm	equivalence of Lp norms of Rademacher series for 0<p<∞ ⓘ two-sided bounds between Lp and Lq norms of random series ⓘ
usedFor	analysis of vector-valued random variables ⓘ bounding tail behavior of random sums ⓘ comparison of Lp norms for random series ⓘ studying geometry of Banach spaces ⓘ studying random series in Banach spaces ⓘ studying type and cotype of Banach spaces ⓘ
usedIn	analysis of random Fourier series ⓘ asymptotic geometric analysis ⓘ high-dimensional probability ⓘ study of empirical processes ⓘ
usesRandomVariables	Gaussian random variables ⓘ Rademacher random variables ⓘ

Referenced by (4)

Full triples — surface form annotated when it differs from this entity's canonical label.

Khinchin–Kahane type inequalities → generalizes → Khinchin–Kahane type inequalities self-linksurface differs ⓘ

this entity surface form: Khinchin inequality

Khinchin–Kahane type inequalities → generalizes → Khinchin–Kahane type inequalities self-linksurface differs ⓘ

this entity surface form: Kahane inequality

Khinchin–Kahane type inequalities → hasVariant → Khinchin–Kahane type inequalities self-linksurface differs ⓘ

this entity surface form: noncommutative Khinchin–Kahane inequalities

Minkowski inequality → isSpecialCaseOf → Khinchin–Kahane type inequalities ⓘ