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DC Field | Value | Language |
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dc.contributor.author | Fredrik Brevig, Ole | - |
dc.contributor.author | Ortega Cerdà, Joaquim | - |
dc.contributor.author | Seip, Kristian | - |
dc.date.accessioned | 2023-07-19T09:25:59Z | - |
dc.date.available | 2023-07-19T09:25:59Z | - |
dc.date.issued | 2023-06-07 | - |
dc.identifier.issn | 1061-0022 | - |
dc.identifier.uri | http://hdl.handle.net/2445/200873 | - |
dc.description.abstract | A Hilbert point in $H^p\left(\mathbb{T}^d\right)$, for $d \geq 1$ and $1 \leq p \leq \infty$, is a nontrivial function $\varphi$ in $H^p\left(\mathbb{T}^d\right)$ such that $\|\varphi\|_{H^p\left(\mathbb{T}^d\right)} \leq\|\varphi+f\|_{H^p\left(\mathbb{T}^d\right)}$ whenever $f$ is in $H^p\left(\mathbb{T}^d\right)$ 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 $H^p\left(\mathrm{~T}^d\right)$, but there are other Hilbert points as well when $d \geq 2$. The case of 1 -homogeneous polynomials is studied in depth and, as a byproduct, a new proof is given for the sharp Khinchin inequality for Steinhaus variables in the range $2<p<\infty$. Briefly, the dynamics of a certain nonlinear projection operator is treated. This operator characterizes Hilbert points as its fixed points. An example is exhibited of a function $\varphi$ that is a Hilbert point in $H^p\left(\mathbb{T}^3\right)$ for $p=2,4$, but not for any other $p$; this is verified rigorously for $p>4$ but only numerically for $1 \leq p<4$. | - |
dc.format.extent | 21 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Mathematical Society (AMS) | - |
dc.relation.isformatof | Versió postprint del document publicat a: https://doi.org/10.1090/spmj/1760 | - |
dc.relation.ispartof | St Petersburg Mathematical Journal, 2023, vol. 34, num. 3, p. 405-425 | - |
dc.relation.uri | https://doi.org/10.1090/spmj/1760 | - |
dc.rights | (c) Brevig, O. F. et al., 2023 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Espais de Hardy | - |
dc.subject.classification | Funcions de variables complexes | - |
dc.subject.classification | H-espais | - |
dc.subject.classification | Anàlisi harmònica | - |
dc.subject.classification | Desigualtats (Matemàtica) | - |
dc.subject.other | Hardy spaces | - |
dc.subject.other | Functions of complex variables | - |
dc.subject.other | H-espaces | - |
dc.subject.other | Harmonic analysis | - |
dc.subject.other | Inequalities (Mathematics) | - |
dc.title | Hilbert points in Hardy spaces | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/acceptedVersion | - |
dc.identifier.idgrec | 737224 | - |
dc.date.updated | 2023-07-19T09:25:59Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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737224.pdf | 435.61 kB | Adobe PDF | View/Open |
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