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 $\widehat$ is the Fourier transform of .

The Beppo Levi space is

:$\dot^ = \left \.$

An alternative definition is as follows: let such that

: $-m + \tfrac < s < \tfrac$

and define:

:\begin
H^s &= \left \ \\ ptX^ &= \left \ \\
\end

Then is the Beppo-Levi space.

References

* Wendland, Holger (2005), ''Scattered Data Approximation'', Cambridge University Press.
* Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2007), "An extension of a bound for functions in Sobolev spaces, with applications to (m,s)-spline interpolation and smoothing" ''Numerische Mathematik''
* Rémi Arcangéli; María Cruz López de Silanes; Juan José Torrens (2009), "Estimates for functions in Sobolev spaces defined on unbounded domains" ''Journal of Approximation Theory''

External links

* L. Brasco, D. Gómez-Castro, J.L. Vázquez, Characterisation of homogeneous fractional Sobolev spaces https://link.springer.com/content/pdf/10.1007/s00526-021-01934-6.pdf
* J. Deny, J.L. Lions, Les espaces du type de Beppo-Levy https://aif.centre-mersenne.org/item/10.5802/aif.55.pdf
* R. Adams, J. Fournier, Sobolev Spaces (2003), Academic press -- Theorem 4.31

Functional analysis

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