تقرير
Hilbert points in Hardy spaces
| العنوان: | Hilbert points in Hardy spaces |
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| المؤلفون: | Brevig, Ole Fredrik, Ortega-Cerdà, Joaquim, Seip, Kristian |
| المصدر: | Algebra i Analiz 34 (2022), no. 3, 131--158 or St. Petersburg Math. J. 34 (2023), no. 3, 405--425 |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Functional Analysis, Mathematics - Classical Analysis and ODEs, Mathematics - Complex Variables |
| الوصف: | A Hilbert point in $H^p(\mathbb{T}^d)$, for $d\geq1$ and $1\leq p \leq \infty$, is a nontrivial function $\varphi$ in $H^p(\mathbb{T}^d)$ such that $\| \varphi \|_{H^p(\mathbb{T}^d)} \leq \|\varphi + f\|_{H^p(\mathbb{T}^d)}$ whenever $f$ is in $H^p(\mathbb{T}^d)$ and orthogonal to $\varphi$ in the usual $L^2$ sense. When $p\neq 2$, $\varphi$ is a Hilbert point in $H^p(\mathbb{T})$ if and only if $\varphi$ is a nonzero multiple of an inner function. An inner function on $\mathbb{T}^d$ is a Hilbert point in any of the spaces $H^p(\mathbb{T}^d)$, but there are other Hilbert points as well when $d\geq 2$. We investigate the case of $1$-homogeneous polynomials in depth and obtain as a byproduct a new proof of the sharp Khintchin inequality for Steinhaus variables in the range $2 Comment: This paper has been accepted for publication in Algebra and Analysis |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1090/spmj/1760 |
| URL الوصول: | http://arxiv.org/abs/2106.07532 |
| رقم الأكسشن: | edsarx.2106.07532 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1090/spmj/1760 |
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