# Besov spaces on open sets

```@inproceedings{Iwabuchi2016BesovSO,
title={Besov spaces on open sets},
author={Tsukasa Iwabuchi and Tokio Matsuyama and Koichi Taniguchi},
year={2016}
}```
This paper is devoted to giving definitions of Besov spaces on an arbitrary open set of \$\mathbb R^n\$ via the spectral theorem for the Schr\"odinger operator with the Dirichlet boundary condition. The crucial point is to introduce some test function spaces on \$\Omega\$. The fundamental properties of Besov spaces are also shown, such as embedding relations and duality, etc. Furthermore, the isomorphism relations are established among the Besov spaces in which regularity of functions is measured… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 26 REFERENCES

## Heat kernel based decomposition of spaces of distributions in the framework of Dirichlet spaces

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

## Decomposition of Besov Spaces

VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

VIEW 1 EXCERPT

VIEW 1 EXCERPT

VIEW 1 EXCERPT

VIEW 1 EXCERPT