On the Generalized Weighted Lebesgue Spaces of Locally Compact Groups

الملخص EN

Let G be a locally compact group with a fixed left Haar measure λ and Ω be a system of weights on G.

In this paper, we deal with locally convex space Lp(G,Ω) equipped with the locally convex topology generated by the family of norms (‖.‖p,ω)ω∈Ω.

We study various algebraic and topological properties of the locally convex space Lp(G,Ω).

In particular, we characterize its dual space and show that it is a semireflexive space.

Finally, we give some conditions under which Lp(G,Ω) with the convolution multiplication is a topological algebra and then characterize its closed ideals and its spectrum.