Abstract and Applied Analysis

Some Intersections of the Weighted L p -Spaces

F. Abtahi, H. G. Amini, H. A. Lotfi, and A. Rejali

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Let G be a locally compact group Ω an arbitrary family of the weight functions on G, and 1 p < . The locally convex space I L p ( G , Ω ) as a subspace of ω Ω L p ( G , ω ) is defined. Also, some sufficient conditions for that space to be a Banach space are provided. Furthermore, for an arbitrary subset J of [ 1 , ) and a positive submultiplicative weight function ω on G , Banach subspace I L J ( G , ω ) of p J L p ( G , ω ) is introduced. Then some algebraic properties of I L J ( G , ω ) , as a Banach algebra under convolution product, are investigated.

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

First available in Project Euclid: 27 February 2014

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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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