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On optimal endpoints for integral kernel operators

  • Ivan Kotalík
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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 Calderón operator given by this pointwise estimate. We use these results to propose optimal endpoint spaces for some integral kernel operators.

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Cite

BibTeXRIS
BibTeX
@misc{kotalik2026optimal,
  title = {{On optimal endpoints for integral kernel operators}},
  author = {Ivan Kotalík},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.05070},
  eprint = {2607.05070},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.05070},
}
RIS
TY  - UNPB
TI  - On optimal endpoints for integral kernel operators
AU  - Ivan Kotalík
PY  - 2026
DA  - 2026/09/12
PB  - arXiv
DO  - 10.48550/arxiv.2607.05070
UR  - https://arxiv.org/abs/2607.05070
AB  - 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.
ER  -