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Critical molecular theory and the maximal admissible class for Goldberg-type splittings of hp(ℝn), 0<p≤ 1

  • Mohamed El Aoumari
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Abstract

We extend the classical Taibleson-Weiss molecular theory to arbitrary radii, reaching the critical decay |x|^{-n/p}, with the resulting embedding shown sharp. This molecular theory governs the largest class of functions certifying membership in h^p(R^n), 0 < p <= 1, through Goldberg's convolution splitting: a critical Hölder modulus and an \ell^p-Dini decay majorant, sharp on the regularity, decay, and cancellation axes.

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Cite

BibTeXRIS
BibTeX
@misc{aoumari2026critical,
  title = {{Critical molecular theory and the maximal admissible class for Goldberg-type splittings of $h^p(\mathbbR^n)$, $0<p\le 1$}},
  author = {Mohamed El Aoumari},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.14960},
  eprint = {2608.14960},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.14960},
}
RIS
TY  - UNPB
TI  - Critical molecular theory and the maximal admissible class for Goldberg-type splittings of h^p(ℝ^n), 0<p≤ 1
AU  - Mohamed El Aoumari
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.14960
UR  - https://arxiv.org/abs/2608.14960
AB  - We extend the classical Taibleson-Weiss molecular theory to arbitrary radii, reaching the critical decay |x|^{-n/p}, with the resulting embedding shown sharp. This molecular theory governs the largest class of functions certifying membership in h^p(R^n), 0 < p <= 1, through Goldberg's convolution splitting: a critical Hölder modulus and an \ell^p-Dini decay majorant, sharp on the regularity, decay, and cancellation axes.
ER  -