Global Stein Theorem on Hardy spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911012481925120 |
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| author | Bonami, Aline Grellier, Sandrine Sehba, Benoit |
| author_facet | Bonami, Aline Grellier, Sandrine Sehba, Benoit |
| contents | Let f be an integrable function which has integral 0 on R n. What is the largest condition on |f | that guarantees that f is in the Hardy space H 1 (R n)? When f is compactly supported, it is well-known that it is necessary and sufficient that |f | belongs to L log L(R n). We are interested here in conditions at $\infty$. We do so for H 1 (R n), as well as for the Hardy space H log (R n) which appears in the study of pointwise products of functions in H 1 (R n) and in its dual BMO. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03595 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Global Stein Theorem on Hardy spaces Bonami, Aline Grellier, Sandrine Sehba, Benoit Classical Analysis and ODEs Let f be an integrable function which has integral 0 on R n. What is the largest condition on |f | that guarantees that f is in the Hardy space H 1 (R n)? When f is compactly supported, it is well-known that it is necessary and sufficient that |f | belongs to L log L(R n). We are interested here in conditions at $\infty$. We do so for H 1 (R n), as well as for the Hardy space H log (R n) which appears in the study of pointwise products of functions in H 1 (R n) and in its dual BMO. |
| title | Global Stein Theorem on Hardy spaces |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2209.03595 |