Some intersections of the weighted Lp -spaces

Abstract

Let G be a locally compact group Ω an arbitrary family of the weight functions on G, and 1≤p<∞. The locally convex space ILp(G,Ω) as a subspace of ∩ω∈ΩLp(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 ILJ(G,ω) of ∩p∈JLp(G,ω) is introduced. Then some algebraic properties of ILJ(G,ω), as a Banach algebra under convolution product, are investigated. © 2013 F. Abtahi et al.