Contractive projections, conditional expectations, and idempotent coefficient multipliers on $H^p$ spaces $(0<p<1)$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918140898705408 |
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| author | Fu, Xiangdi Guo, Kunyu Li, Dilong |
| author_facet | Fu, Xiangdi Guo, Kunyu Li, Dilong |
| contents | In this paper, we investigate contractive projections, conditional expectations, and idempotent coefficient multipliers on the Hardy spaces $H^p(\mathbb{T})$ for $0<p<1$. For such values of $p$, we first establish a general extension theorem for contractive projections in a probability $L^p$-space. Combining this theorem with the study of conditional expectations on $H^p(\mathbb{T})$, we characterize a broad class of contractive projections on $H^p(\mathbb{T})$ that are of particular interest. Furthermore, we apply these results to give a complete characterization of contractive idempotent coefficient multipliers for the Hardy spaces $H^p(\mathbb{T}^d)$ on the $d$-dimensional torus for $0<p<1$ and $1\leq d\leq \infty$. This complements a remarkable result of Brevig, Ortega-Cerdà, and Seip characterizing such multipliers on $H^p(\mathbb{T}^d)$ for $1\leq p \leq \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06615 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Contractive projections, conditional expectations, and idempotent coefficient multipliers on $H^p$ spaces $(0<p<1)$ Fu, Xiangdi Guo, Kunyu Li, Dilong Functional Analysis In this paper, we investigate contractive projections, conditional expectations, and idempotent coefficient multipliers on the Hardy spaces $H^p(\mathbb{T})$ for $0<p<1$. For such values of $p$, we first establish a general extension theorem for contractive projections in a probability $L^p$-space. Combining this theorem with the study of conditional expectations on $H^p(\mathbb{T})$, we characterize a broad class of contractive projections on $H^p(\mathbb{T})$ that are of particular interest. Furthermore, we apply these results to give a complete characterization of contractive idempotent coefficient multipliers for the Hardy spaces $H^p(\mathbb{T}^d)$ on the $d$-dimensional torus for $0<p<1$ and $1\leq d\leq \infty$. This complements a remarkable result of Brevig, Ortega-Cerdà, and Seip characterizing such multipliers on $H^p(\mathbb{T}^d)$ for $1\leq p \leq \infty$. |
| title | Contractive projections, conditional expectations, and idempotent coefficient multipliers on $H^p$ spaces $(0<p<1)$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2503.06615 |