Khinchin–Kahane type inequalities

E87730

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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Generate an image of Khinchin–Kahane type inequalities (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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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 Kahane inequality ⓘ
Khinchin inequality ⓘ
hasProperty constants depend on p but not on number of terms ⓘ
dimension-free constants in many formulations ⓘ
hasVariant 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 ⓘ
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 ⓘ

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Referenced by (5)

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

Minkowski inequality → isSpecialCaseOf → Khinchin–Kahane type inequalities ⓘ
Khinchin–Kahane type inequalities → generalizes → Khinchin inequality ⓘ
linked to: Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities → generalizes → Kahane inequality ⓘ
linked to: Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities → hasVariant → noncommutative Khinchin–Kahane inequalities ⓘ
linked to: Khinchin–Kahane type inequalities
Grothendieck inequality → relatedTo → Khintchine inequality ⓘ
linked to: Khinchin–Kahane type inequalities