Hardy–Littlewood maximal function
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
For a locally integrable function f on R^n, the maximal function Mf(x) is defined as the supremum over all balls B containing x of the average of |f| over B.
|
| gptkbp:field |
harmonic analysis
mathematical analysis |
| gptkbp:generalizes |
fractional maximal function
one-dimensional maximal function vector-valued maximal function |
| https://www.w3.org/2000/01/rdf-schema#label |
Hardy–Littlewood maximal function
|
| gptkbp:introducedIn |
20th century
|
| gptkbp:namedAfter |
gptkb:G._H._Hardy
gptkb:J._E._Littlewood |
| gptkbp:property |
bounded on L^p for p > 1
sublinear operator weak type (1,1) operator |
| gptkbp:relatedTo |
gptkb:Lebesgue_differentiation_theorem
maximal inequality |
| gptkbp:usedIn |
differentiation theory
real analysis singular integrals |
| gptkbp:bfsParent |
gptkb:G._H._Hardy
gptkb:J._E._Littlewood gptkb:John_Edensor_Littlewood |
| gptkbp:bfsLayer |
5
|