Page 1 Next

Displaying 1 – 20 of 31

Showing per page

On a class of convolution algebras of functions

Hans G. Feichtinger (1977)

Annales de l'institut Fourier

The Banach spaces Λ ( A , B , X , G ) defined in this paper consist essentially of those elements of L 1 ( G ) ( G being a locally compact group) which can in a certain sense be well approximated by functions with compact support. The main result of this paper is the fact that in many cases Λ ( A , B , X , G ) becomes a Banach convolution algebra. There exist many natural examples. Furthermore some theorems concerning inclusion results and the structure of these spaces are given. In particular we prove that simple conditions imply the existence...

On certain porous sets in the Orlicz space of a locally compact group

Ibrahim Akbarbaglu, Saeid Maghsoudi (2012)

Colloquium Mathematicae

Let G be a locally compact group with a fixed left Haar measure. Given Young functions φ and ψ, we consider the Orlicz spaces L φ ( G ) and L ψ ( G ) on a non-unimodular group G, and, among other things, we prove that under mild conditions on φ and ψ, the set ( f , g ) L φ ( G ) × L ψ ( G ) : f * g is well defined on G is σ-c-lower porous in L φ ( G ) × L ψ ( G ) . This answers a question raised by Głąb and Strobin in 2010 in a more general setting of Orlicz spaces. We also prove a similar result for non-compact locally compact groups.

On the Hausdorff-Young theorem for commutative hypergroups

Sina Degenfeld-Schonburg (2013)

Colloquium Mathematicae

We study the Hausdorff-Young transform for a commutative hypergroup K and its dual space K̂ by extending the domain of the Fourier transform so as to encompass all functions in L p ( K , m ) and L p ( K ̂ , π ) respectively, where 1 ≤ p ≤ 2. Our main theorem is that those extended transforms are inverse to each other. In contrast to the group case, this is not obvious, since the dual space K̂ is in general not a hypergroup itself.

Currently displaying 1 – 20 of 31

Page 1 Next