arXiv subjects

Ivan Kotalík

Publications and source records attributed to Ivan Kotalík.

3 recordsLinked to original sources

arXiv2026

On optimal endpoints for integral kernel operators

In this paper, we study the behavior of integral kernel operators acting on functions of a single real variable. In particular, we attempt to find possible candidates for their optimal endpoint spaces in the class of Banach spaces endowed with a rearrangement-invariant quasinorm. To achieve this, we characterize the existence of a concrete pointwise estimate for their nonincreasing rearrangement. We also build a theory of optimal endpoint spaces for the Calderón operator given by this pointwise estimate. We use these results to propose optimal endpoint spaces for some integral kernel operators.

math.FA↗

arXiv2026

Amalgam approach to compactness in (quasi-)Banach function spaces

We present amalgam-type characterisations of compactness in quasi-Banach function spaces. We further treat, in the same spirit, several related topics, namely convergence, (uniform) absolute continuity of the norm, and almost-compact embeddings. We also treat the case of rearrangement-invariant spaces and show that most of our conditions can be formulated in terms of the non-increasing rearrangement and the representation space.

math.FA↗

arXiv2026

Wiener--Luxemburg amalgam spaces revisited

The fundamental reliance on nonincreasing rearrangements restricts the recently introduced Wiener--Luxemburg amalgam spaces only to the rearrangement-invariant setting. To overcome this barrier, we develop a novel comprehensive framework that expands these amalgam structures to arbitrary quasi-Banach function spaces. By constructing a new quasinorm based on measure-constrained suprema and infima, we successfully separate these amalgams from rearrangement theory. We resolve the ensuing structural challenges regarding the Fatou property in this generalized setting, show consistency with the original theory, and fully characterize associate spaces, continuous embeddings, and the absolute continuity of the norm.

math.FA↗