The Multipliers for Functions with Fourier Transforms in Lp.
For we calculate the norm of the Fourier transform from the space on a finite abelian group to the space on the dual group.
Let A be a commutative Banach algebra and let be its structure space. The norm spectrum σ(f) of the functional f ∈ A* is defined by , where f·a is the functional on A defined by ⟨f·a,b⟩ = ⟨f,ab⟩, b ∈ A. We investigate basic properties of the norm spectrum in certain classes of commutative Banach algebras and present some applications.
Let be a locally compact group, and let be a function norm on such that the space of all locally integrable functions with finite -norm is an invariant solid Banach function space. Consider the space of all functions in of which the right translation is a continuous map from into . Characterizations of the case where is a Riesz ideal of are given in terms of the order-continuity of on certain subspaces of . Throughout the paper, the discussion is carried out in the context...
We prove that in order to describe the Poisson boundary of rational affinities, it is necessary and sufficient to consider the action on real and all -adic fileds.