Triebel–Lizorkin space

In the mathematical discipline known as functional analysis, a Triebel–Lizorkin space is a generalization of many standard function spaces such as L^p spaces and Sobolev spaces. It is named after Hans Triebel (born February 7th 1936 in Dessau) and Petr Ivanovich Lizorkin.

External links

Homogeneity Property of Besov and Triebel-Lizorkin Spaces

References

Peetre, Jaak (1975), "On spaces of Triebel–Lizorkin type", Arkiv för Matematik, 13 (1–2): 123–130, doi:10.1007/BF02386201.
Kalton, N., Interpolation of Hardy-Sobolev-Besov-Triebel-Lizorkin Spaces and Applications to Problems in Partial Differential Equations (PDF)

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Functional analysis (topics, glossary)
Spaces	Hilbert space, Banach space, Fréchet space, topological vector space
Theorems	Hahn–Banach theorem, closed graph theorem, uniform boundedness principle, Kakutani fixed-point theorem, Krein–Milman theorem, min-max theorem, Gelfand–Naimark theorem, Banach–Alaoglu theorem
Operators	bounded operator, compact operator, adjoint operator, unitary operator, Hilbert–Schmidt operator, trace class, unbounded operator
Algebras	Banach algebra, C-algebra, spectrum of a C-algebra, operator algebra, group algebra of a locally compact group, von Neumann algebra
Open problems	invariant subspace problem, Mahler's conjecture
Applications	Besov space, Hardy space, spectral theory of ordinary differential equations, heat kernel, index theorem, calculus of variation, functional calculus, integral operator, Jones polynomial, topological quantum field theory, noncommutative geometry, Riemann hypothesis
Advanced topics	locally convex space, approximation property, balanced set, Schwartz space, weak topology, barrelled space, Banach–Mazur distance, Tomita–Takesaki theory