Fractional integral on Hardy spaces on product domains
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915758329561088 |
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| author | Tang, Yiyu |
| author_facet | Tang, Yiyu |
| contents | By using the vector-valued theory of singular integrals, we prove a Hardy--Littlewood--Sobolev inequality on product Hardy spaces $H^p_{\rm{prod}}$, which is a parallel result of the classical Hardy--Littlewood--Sobolev inequality. The same technique shows the $H^p_{\rm{prod}}$-boundedness of the iterated Hilbert transform. As a byproduct, new proofs of several recently discovered Hardy type inequalities on product Hardy spaces are obtained, which avoid complicated Calderón--Zygmund theory on product domain, rendering them considerably simpler than the original proofs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03158 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fractional integral on Hardy spaces on product domains Tang, Yiyu Functional Analysis Classical Analysis and ODEs By using the vector-valued theory of singular integrals, we prove a Hardy--Littlewood--Sobolev inequality on product Hardy spaces $H^p_{\rm{prod}}$, which is a parallel result of the classical Hardy--Littlewood--Sobolev inequality. The same technique shows the $H^p_{\rm{prod}}$-boundedness of the iterated Hilbert transform. As a byproduct, new proofs of several recently discovered Hardy type inequalities on product Hardy spaces are obtained, which avoid complicated Calderón--Zygmund theory on product domain, rendering them considerably simpler than the original proofs. |
| title | Fractional integral on Hardy spaces on product domains |
| topic | Functional Analysis Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2509.03158 |