Lebesgue spaces

GPTKB entity

Statements (29)
Predicate Object
gptkbp:instanceOf 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
https://www.w3.org/2000/01/rdf-schema#label Lebesgue spaces
gptkbp:importantFor gptkb:interpolation_theory
Fourier analysis
partial differential equations
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