On p-Dunford integrable functions with values in Banach spaces

Abstract

Let (Ω, Σ, µ) be a complete probability space, X a Banach space and 1 ≤ p < ∞. In this paper we discuss several aspects of p-Dunford integrable functions f : Ω → X. Special attention is paid to the compactness of the Dunford operator of f . We also study the p-Bochner integrability of the composition u • f : Ω → Y , where u is a p-summing operator from X to another Banach space Y . Finally, we also provide some tests of p-Dunford integrability by using w * -thick subsets of X * .

On the solutions of Caputo–Hadamard Pettis-type fractional differential equations

“…Recall that (see e.g. [8][9][10][11][12][13][14][15]) the weakly measurable function x : I → E is said to be ψ-Dunford (where ψ is a Young function) integrable on I if and only if ϕx ∈ L ψ (I ) for each ϕ ∈ E * .…”