Beppo-Levi space

In functional analysis, a branch of mathematics, a Beppo Levi space, named after Beppo Levi, is a certain space of generalized functions.

In the following, D′ is the space of distributions, S′ is the space of tempered distributions in Rn, Dα the differentiation operator with α a multi-index, and

is the Fourier transform of v. The Beppo Levi space is where |⋅|r,p denotes the Sobolev semi-norm.

An alternative definition is as follows: let m ∈ N, s ∈ R such that and define: Then Xm,s is the Beppo-Levi space.

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