Triebel–Lizorkin space
Encyclopedia
In the mathematical discipline known as functional analysis
, a Triebel–Lizorkin space is a generalization of many standard function spaces such as Lp spaces
and Sobolev space
s. It is named after Hans Triebel and Petr Ivanovich Lizorkin.
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, a Triebel–Lizorkin space is a generalization of many standard function spaces such as Lp spaces
Lp space
In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces...
and Sobolev space
Sobolev space
In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function itself as well as its derivatives up to a given order. The derivatives are understood in a suitable weak sense to make the space complete, thus a Banach space...
s. It is named after Hans Triebel and Petr Ivanovich Lizorkin.