## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Weighted $L^p-$spaces on locally compact groups

Fatemeh Abtahi

#### Abstract

Let $G$ be a locally compact group, $\omega$ be a weight function on $G$ and $0<p<1$. We investigate the space $L^p(G,\omega){\star}L^p(G,\omega)$ as a subset of some special spaces such as $L^p(G,\omega)$, $L^{\infty}(G,1/\widetilde{\omega})$ and $C_0(G,1/\widetilde{\omega})$. As the main result we show that all of the mentioned inclusions are equivalent to the discreteness of $G$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 19, Number 2 (2012), 339-343.

Dates
First available in Project Euclid: 24 May 2012

https://projecteuclid.org/euclid.bbms/1337864277

Digital Object Identifier
doi:10.36045/bbms/1337864277

Mathematical Reviews number (MathSciNet)
MR2977236

Zentralblatt MATH identifier
1245.43001

#### Citation

Abtahi, Fatemeh. Weighted $L^p-$spaces on locally compact groups. Bull. Belg. Math. Soc. Simon Stevin 19 (2012), no. 2, 339--343. doi:10.36045/bbms/1337864277. https://projecteuclid.org/euclid.bbms/1337864277