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arXiv · 2607.22826

Weak-$A_\infty$ packing and estimates for fractional sparse forms on spaces of homogeneous type

Hanwen Zhang
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Abstract

We prove two-weight estimates for fractional sparse forms on spaces of homogeneous type. The relevant transformed weights are assumed to belong to weak-$A_\infty$. The weak reverse H\"older inequality is normalized on enlarged balls, while sparse testing is normalized on dyadic cubes. To measure this loss, we introduce $\mathfrak d_Q^w:=w(Q)/w(2\Lambda B_Q)$. A packing estimate for the defect levels, combined with two-weight testing, gives the required mixed weak-$A_\infty$ bounds.

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Hanwen Zhang. 2026-07-24. Weak-$A_\infty$ packing and estimates for fractional sparse forms on spaces of homogeneous type. https://arxiv.org/abs/2607.22826

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