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arXiv · 2610.16123

Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a $C^{1,\mathrm{Dini}}$ curve

Ji Li·Chun-Yen Shen·Eric Sawyer·Brett Wick
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Abstract

Let $0\leqα n-3$ in a bounded tube and $n-3<β<n-2$ in $\R^n$. The endpoints fail logarithmically whenever the measure is locally finite. In dimension three, the corresponding whole-space range for the Biot--Savart field with arbitrary vector densities is $0<β<1$.

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Ji Li, Chun-Yen Shen, Eric Sawyer, Brett Wick. 2026-10-12. Two-weight T1 theorem for fractional Riesz transforms: one measure supported on a $C^{1,\mathrm{Dini}}$ curve. https://arxiv.org/abs/2610.16123

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