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, is the space of distributions, is the space of tempered distributions in, the differentiation operator with a multi-index, and is the Fourier transform of.
The Beppo Levi space is
An alternative definition is as follows: let such that
and define:
Then is the Beppo-Levi space.