José Luis and I first met at the famous - and hugely enjoyable 1983 El Escorial conference of which he and Ireneo Peral were the chief organisers, but we did not really discuss mathematics together until the spring and summer of 1985. There is an old question - formally posed by Stein in the proceedings of the 1978 Williamstown conference [St] - concerning the disc multiplier and the Bochner-Riesz means.
Let ⟨X,Y⟩ be a duality pair of M-spaces X,Y of measurable functions from Ω ⊂ ℝ ⁿ into . The paper deals with Y-weak cluster points ϕ̅ of the sequence in X, where is measurable for j ∈ ℕ and is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set , the integral exists for and on , where is a measurable-dependent family of Radon probability measures on .
An integral transform denoted by that generalizes the well-known Laplace and Meijer transformations, is studied in this paper on certain spaces of generalized functions introduced by A.C. McBride by employing the adjoint method.
The -property of a Riesz space (real vector lattice) is: For each sequence of positive elements of , there is a sequence of positive reals, and , with for each . This condition is involved in studies in Riesz spaces of abstract Egoroff-type theorems, and of the countable lifting property. Here, we examine when “” obtains for a Riesz space of continuous real-valued functions . A basic result is: For discrete , has iff the cardinal , Rothberger’s bounding number. Consequences and...
In this paper we introduce the notion of topological G-spaces. This is an intermediate class between G-sets and A-modules. After giving suitable definitions and illustrating examples, we prove a theorem of closed graph theorem type.