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arXiv · 2608.14960

Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$

Mohamed El Aoumari
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Abstract

We identify the largest class of functions certifying membership in $h^p(\mathbb{R}^n)$, $0<p\le 1$, through Goldberg's convolution splitting: a critical H\"older modulus and an $\ell^p$-Dini decay majorant, sharp on the regularity, decay, and cancellation axes. The class reaches the critical decay $|x|^{-n/p}$, governed by a molecular theory extending the classical Taibleson-Weiss theory to every radius, with the resulting embedding shown sharp.

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Mohamed El Aoumari. 2026-08-15. Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbb{R}^n)$, $0<p\le 1$. https://arxiv.org/abs/2608.14960

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