Analytic functions on c0.
We continue our study of derivations, multipliers, weak amenability and Arens regularity of Segal algebras on locally compact groups. We also answer two questions on Arens regularity of the Lebesgue-Fourier algebra left open in our earlier work.
Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function is estimated, where and K satisfies a generalized Lipschitz condition with respect to the second variable.
Let X denote the space of all real, bounded double sequences, and let Φ, φ, Γ be φ-functions. Moreover, let Ψ be an increasing, continuous function for u ≥ 0 such that Ψ(0) = 0.In this paper we consider some spaces of double sequences provided with two-modular structure given by generalized variations and the translation operator (...).
We obtain modular convergence theorems in modular spaces for nets of operators of the form , w > 0, s ∈ G, where G and H are topological groups and is a family of homeomorphisms Such operators contain, in particular, a nonlinear version of the generalized sampling operators, which have many applications in the theory of signal processing.