On optimal endpoints for integral kernel operators
Functional Analysis
2026-07-06 v1
Abstract
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 Calder\'on operator given by this pointwise estimate. We use these results to propose optimal endpoint spaces for some integral kernel operators.
Cite
@article{arxiv.2607.05070,
title = {On optimal endpoints for integral kernel operators},
author = {Ivan Kotalík},
journal= {arXiv preprint arXiv:2607.05070},
year = {2026}
}