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 …

We study several properties of the Banach lattices L p (m) and L pw (m) of p-integrable
scalar functions and weakly p-integrable scalar functions with respect to a countably additive …

We study the behaviour on rearrangement-invariant (ri) spaces of such classical operators of
interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the …

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 …

New features of the Banach function space L1w (v), that is, the space of all v-scalarly
integrable functions (with v any vector measure), are exposed. The Fatou property plays an …

In mathematical modelling, the data and solutions are represented as measurable functions
and their quality is oftentimes captured by the membership to a certain function space. One …

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 …

The principle of optimizing inequalities, or their equivalent operator theoretic formulation, is
well established in analysis. For an operator, this corresponds to extending its action to …