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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2503.18232 |
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| _version_ | 1866916660522254336 |
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| author | Mitrea, Dorina Mitrea, Irina Mitrea, Marius |
| author_facet | Mitrea, Dorina Mitrea, Irina Mitrea, Marius |
| contents | We employ the Riesz transform as a means for describing geometric properties of sets in ${\mathbb{R}}^n$, and study the extent to which they can be used to characterize function spaces defined on said sets. In particular, characterizations of the end-point spaces on the Lebesgue scale $L^p$ with $1<p<\infty$, namely the Hardy space $H^1$ and the John-Nirenberg space {\rm BMO}, are produced in terms of the Riesz transforms on Ahlfors regular sets in ${\mathbb{R}}^n$ with small oscillations (quantified in terms of the {\rm BMO} nature of the outward unit normal). These generalize the celebrated results of C.~Fefferman and E.~Stein in the flat Euclidean setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Riesz Transform Characterizations of $H^1$ and {\rm BMO} on Ahlfors Regular Sets with Small Oscillations Mitrea, Dorina Mitrea, Irina Mitrea, Marius Analysis of PDEs Functional Analysis We employ the Riesz transform as a means for describing geometric properties of sets in ${\mathbb{R}}^n$, and study the extent to which they can be used to characterize function spaces defined on said sets. In particular, characterizations of the end-point spaces on the Lebesgue scale $L^p$ with $1<p<\infty$, namely the Hardy space $H^1$ and the John-Nirenberg space {\rm BMO}, are produced in terms of the Riesz transforms on Ahlfors regular sets in ${\mathbb{R}}^n$ with small oscillations (quantified in terms of the {\rm BMO} nature of the outward unit normal). These generalize the celebrated results of C.~Fefferman and E.~Stein in the flat Euclidean setting. |
| title | Riesz Transform Characterizations of $H^1$ and {\rm BMO} on Ahlfors Regular Sets with Small Oscillations |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2503.18232 |