Operator theory and functional analysis have a long tradition, initially being guided by
problems from mathematical physics and applied mathematics. Much of the work in Banach …

Abstract The Orlicz spaces X^\varPhi X Φ associated to a quasi-Banach function space X
are defined by replacing the role of the space L^ 1 L 1 by X in the classical construction of …

We study the optimal domain for the Hardy operator considered with values in a
rearrangement invariant space. In particular, this domain can be represented as the space of …

Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X
is defined as the space of the multipliers from X to Y. The space XY is a generalization of the …

The Cesàro function spaces Ces p=[C, L p], 1≤ p≤∞, have received renewed attention in
recent years. Many properties of [C, L p] are known. Less is known about [C, X] when the …

Abstract Given 1< p< 2, we construct a Banach function space with σ-order continuous norm
which contains and has the property that the Fourier transform map has a continuous ℓ …

In order to extend the theory of optimal domains for continuous operators on a Banach
function space X (μ) over a finite measure μ, we consider operators T satisfying other type of …

We study some Banach lattice properties of the space L_w^ 1 (ν) of weakly integrable
functions with respect to a vector measure ν defined on a δ-ring. Namely, we analyze order …

We will deal exclusively with the integration of scalar (ie, ℝ or ℂ)-valued functions with
respect to vector measures. The general theory can be found in [36, 37, 32],[44, Ch. I II] and …

In 1953, Grothendieck [G] characterized locally convex Hausdorff spaces which have the
Dunford-Pettis property and used this property to characterize weakly compact operators u …