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arXiv · 2610.32671

Sharpness transitions for weighted Triebel--Lizorkin Hardy inequalities with p < q

Yongyang Jin·Li Tang
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Abstract

For fractional difference energies with two power weights and distinct inner and outer exponents, we determine regimes in which the constant generated by the homogeneous power is optimal and regimes in which it loses optimality. In the range $1 q$, including flat-subspace inequalities and a complete alternative proof for point singularities. All sharpness sequences belong to the specified smooth test classes, and every positive optimal constant extends to their completion in the difference norm.

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Yongyang Jin, Li Tang. 2026-10-23. Sharpness transitions for weighted Triebel--Lizorkin Hardy inequalities with p < q. https://arxiv.org/abs/2610.32671

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