English

The Bellman Function for Level Sets of Sparse Operators

Classical Analysis and ODEs 2026-03-16 v2

Abstract

We investigate weak-type (1,1)(1, 1) boundedness of sparse operators with respect to Lebesgue measure. Specifically, we find the Bellman function maximizing level sets of sparse operators (localized to an interval) and use this to find the exact weak-(1,1)(1,1) norm of these sparse operators.

Keywords

Cite

@article{arxiv.2506.12315,
  title  = {The Bellman Function for Level Sets of Sparse Operators},
  author = {Irina Holmes Fay and Zachary H. Pence and John Freeland Small and Xiaokun Zhou},
  journal= {arXiv preprint arXiv:2506.12315},
  year   = {2026}
}

Comments

Final version to appear in IMRN

R2 v1 2026-07-01T03:17:17.797Z