Some Intersections of the Weighted Lp-Spaces

Abstract EN

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.