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http://hdl.handle.net/2445/95822
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DC Field | Value | Language |
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dc.contributor.author | Barza, Sorina | - |
dc.contributor.author | Kolyada, Viktor | - |
dc.contributor.author | Soria de Diego, F. Javier | - |
dc.date.accessioned | 2016-02-24T10:21:10Z | - |
dc.date.available | 2016-02-24T10:21:10Z | - |
dc.date.issued | 2009 | - |
dc.identifier.issn | 0002-9947 | - |
dc.identifier.uri | http://hdl.handle.net/2445/95822 | - |
dc.description.abstract | We study the Lorentz spaces $ L^{p,s}(R,\mu)$ in the range $ 1<p<s\le \infty$, for which the standard functional $\displaystyle \vert\vert f\vert\vert _{p,s}=\left(\int_0^\infty (t^{1/p}f^*(t))^s\frac{dt}{t}\right)^{1/s} $ is only a quasi-norm. We find the optimal constant in the triangle inequality for this quasi-norm, which leads us to consider the following decomposition norm: $\displaystyle \vert\vert f\vert\vert _{(p,s)}=\inf\bigg\{\sum_{k}\vert\vert f_k\vert\vert _{p,s}\bigg\}, $ where the infimum is taken over all finite representations $ f=\sum_{k}f_k. $ We also prove that the decomposition norm and the dual norm $\displaystyle \vert\vert f\vert\vert _{p,s}'= \sup\left\{ \int_R fg d\mu: \vert\vert g\vert\vert _{p',s'}=1\right\}$ agree for all values of $ p,s>1$. | - |
dc.format.extent | 20 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | American Mathematical Society (AMS) | - |
dc.relation.isformatof | Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-09-04739-4 | - |
dc.relation.ispartof | Transactions of the American Mathematical Society, 2009, vol. 361, num. 10, p. 5555-5574 | - |
dc.relation.uri | http://dx.doi.org/10.1090/S0002-9947-09-04739-4 | - |
dc.rights | (c) American Mathematical Society (AMS), 2009 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Anàlisi funcional | - |
dc.subject.classification | Espais de Lorentz | - |
dc.subject.other | Functional analysis | - |
dc.subject.other | Lorentz spaces | - |
dc.title | Sharp constants related to the triangle inequality in Lorentz spaces | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 555509 | - |
dc.date.updated | 2016-02-24T10:21:15Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
Files in This Item:
File | Description | Size | Format | |
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555509.pdf | 280.34 kB | Adobe PDF | View/Open |
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