## Abstract and Applied Analysis

### Some Intersections of the Weighted ${L}^{p}$-Spaces

#### Abstract

Let $G$ be a locally compact group $\mathrm{\Omega }$ an arbitrary family of the weight functions on $\mathrm{G,}$ and $\mathrm{1}\le p<\mathrm{\infty }$. The locally convex space $I{L}_{p}\left(G,\mathrm{\Omega }\right)$ as a subspace of ${\cap }_{\omega \in \mathrm{\Omega }}{L}^{p}\left(G,\omega \right)$ is defined. Also, some sufficient conditions for that space to be a Banach space are provided. Furthermore, for an arbitrary subset $J$ of $\left[\mathrm{1},\mathrm{\infty }\right)$ and a positive submultiplicative weight function $\omega$ on $G$, Banach subspace $I{L}_{J}\left(G,\omega \right)$ of ${\cap }_{p\in J}{L}^{p}\left(G,\omega \right)$ is introduced. Then some algebraic properties of $I{L}_{J}\left(G,\omega \right)$, as a Banach algebra under convolution product, are investigated.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 986857, 12 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393512085

Digital Object Identifier
doi:10.1155/2013/986857

Mathematical Reviews number (MathSciNet)
MR3121403

Zentralblatt MATH identifier
1313.43001

#### Citation

Abtahi, F.; Amini, H. G.; Lotfi, H. A.; Rejali, A. Some Intersections of the Weighted ${L}^{p}$ -Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 986857, 12 pages. doi:10.1155/2013/986857. https://projecteuclid.org/euclid.aaa/1393512085

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