Calderón transference principle
E817948
The Calderón transference principle is a fundamental result in harmonic analysis that allows boundedness properties of operators on one group (often the real line or integers) to be transferred to analogous operators on more general groups or measure spaces.
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical theorem
ⓘ
result in harmonic analysis ⓘ |
| appliesTo |
linear operators
ⓘ
sublinear operators ⓘ |
| assumption | uniform bounds on operators in the model setting ⓘ |
| conclusion | corresponding bounds for induced operators in the abstract setting ⓘ |
| field |
functional analysis
ⓘ
harmonic analysis ⓘ |
| framework | L^p spaces ⓘ |
| generalizedBy |
non-commutative transference principles
ⓘ
vector-valued transference principles ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| influenced |
development of abstract harmonic analysis
ⓘ
study of operators on non-commutative groups ⓘ |
| involves |
covariance of operators with respect to group actions
ⓘ
intertwining of representations ⓘ |
| mainIdea | transfers boundedness properties of operators between groups or measure spaces ⓘ |
| namedAfter | Alberto Calderón NERFINISHED ⓘ |
| propertyTransferred |
L^p boundedness
ⓘ
maximal inequalities ⓘ weak-type estimates ⓘ |
| relatedConcept |
Fourier multiplier theorems
NERFINISHED
ⓘ
ergodic averages ⓘ maximal function estimates ⓘ |
| relates | operators on model groups to operators on abstract groups ⓘ |
| requires |
measure-preserving group action
ⓘ
representation of the group on a function space ⓘ |
| sourceSetting |
integers
ⓘ
real line ⓘ |
| status | standard tool in modern harmonic analysis ⓘ |
| targetSetting |
general groups
ⓘ
general measure spaces ⓘ |
| typicalDomain |
locally compact abelian groups
ⓘ
measure spaces with group actions ⓘ |
| typicalModelGroup |
integer group Z
GENERATED
ⓘ
real line R GENERATED ⓘ |
| usedFor |
Fourier multipliers on groups
ⓘ
convolution operators on groups ⓘ ergodic theorems ⓘ maximal ergodic inequalities ⓘ singular integral operators on groups ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.