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arXiv · 2506.12315

The Bellman Function for Level Sets of Sparse Operators

Irina Holmes Fay·Zachary H. Pence·John Freeland Small·Xiaokun Zhou
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Abstract

We investigate weak-type $(1, 1)$ 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-$(1,1)$ norm of these sparse operators.

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Irina Holmes Fay, Zachary H. Pence, John Freeland Small, Xiaokun Zhou. 2025-06-14. The Bellman Function for Level Sets of Sparse Operators. https://arxiv.org/abs/2506.12315

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