Statements (29)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:function_space
|
| gptkbp:alsoKnownAs |
L^p spaces
|
| gptkbp:contains |
measurable functions
|
| gptkbp:definedIn |
measure space
|
| gptkbp:generalizes |
gptkb:Hilbert_space
sequence spaces |
| gptkbp:hasDualSpace |
L^q space (where 1/p + 1/q = 1, 1 < p < ∞)
|
| gptkbp:heldBy |
gptkb:Hilbert_space
gptkb:Vector complete metric space |
| gptkbp:importantFor |
gptkb:partial_differential_equations
gptkb:interpolation_theory Fourier analysis Banach space theory |
| gptkbp:introducedIn |
early 20th century
|
| gptkbp:L^1_space |
integrable functions
|
| gptkbp:L^2_space |
gptkb:Hilbert_space
|
| gptkbp:L^∞_space |
essentially bounded functions
|
| gptkbp:namedAfter |
gptkb:Henri_Lebesgue
|
| gptkbp:normedBy |
L^p norm
|
| gptkbp:parameter |
p
|
| gptkbp:range |
1 ≤ p ≤ ∞
|
| gptkbp:usedIn |
gptkb:probability_theory
functional analysis measure theory |
| gptkbp:bfsParent |
gptkb:Hardy–Littlewood–Sobolev_inequality
gptkb:Lp_spaces |
| gptkbp:bfsLayer |
6
|
| https://www.w3.org/2000/01/rdf-schema#label |
Lebesgue spaces
|