Polarized Hardy--Stein identity
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910788372922368 |
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| author | Bogdan, Krzysztof Gutowski, Michał Pietruska-Pałuba, Katarzyna |
| author_facet | Bogdan, Krzysztof Gutowski, Michał Pietruska-Pałuba, Katarzyna |
| contents | We prove the Hardy--Stein identity for vector functions in $L^p(\mathbb R^d;\mathbb R^n)$ with $1<p<\infty$ and for the canonical paring of two real functions in $L^p(\mathbb R^d)$ with $2\le p<\infty$. To this end we propose a notion of Bregman co-divergence and study the corresponding integral forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09856 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polarized Hardy--Stein identity Bogdan, Krzysztof Gutowski, Michał Pietruska-Pałuba, Katarzyna Classical Analysis and ODEs Functional Analysis Probability Primary 46E35, Secondary 31C05 We prove the Hardy--Stein identity for vector functions in $L^p(\mathbb R^d;\mathbb R^n)$ with $1<p<\infty$ and for the canonical paring of two real functions in $L^p(\mathbb R^d)$ with $2\le p<\infty$. To this end we propose a notion of Bregman co-divergence and study the corresponding integral forms. |
| title | Polarized Hardy--Stein identity |
| topic | Classical Analysis and ODEs Functional Analysis Probability Primary 46E35, Secondary 31C05 |
| url | https://arxiv.org/abs/2309.09856 |