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 …

Sobolev embeddings, rearrangement-invariant spaces and Frostman measures Page 1
Available online at www.sciencedirect.com ScienceDirect Ann. IH Poincaré – AN 37 (2020) …

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 …

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 …

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 …

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 …

Compactness properties of Sobolev imbeddings are studied within the context of
rearrangement invariant norms. Attention is focused on the extremal situation, namely, when …

Given a vector measure m with values in a Banach space X, a desirable property (when
available) of the associated Banach function space L¹ (m) of all m-integrable functions is that …

arXiv:2310.10228v1 [math.FA] 16 Oct 2023 Page 1 arXiv:2310.10228v1 [math.FA] 16 Oct
2023 THE FINITE HILBERT TRANSFORM ON (−1, 1) GUILLERMO P. CURBERA, SUSUMU …

The aim of this article is to study the largest domain space $[T, X] $, whenever it exists, of a
given continuous linear operator $ T\colon X\to X $, where $ X\subseteq H (\mathbb {D}) $ is …