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arXiv · 2601.17068

Sharp $L^p$ Convergence for Mirror-Degenerate Expansions

Francesco D'Agostino
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Abstract

We analyze weighted $L^p$ convergence for the truncated reconstruction operator in the rank-one non-symmetric Heckman--Opdam setting. After localization at the mirror, the operator admits a rigid structural decomposition and reduces, up to bounded terms, to a rank-one functional. Boundedness on $L^p(w)$ is characterized by the mirror-local integrability of $w^{-\frac{1}{p-1}}$.

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Francesco D'Agostino. 2026-01-22. Sharp $L^p$ Convergence for Mirror-Degenerate Expansions. https://arxiv.org/abs/2601.17068

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