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http://hdl.handle.net/2445/95822
Title: | Sharp constants related to the triangle inequality in Lorentz spaces |
Author: | Barza, Sorina Kolyada, Viktor Soria de Diego, F. Javier |
Keywords: | Anàlisi funcional Espais de Lorentz Functional analysis Lorentz spaces |
Issue Date: | 2009 |
Publisher: | American Mathematical Society (AMS) |
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$. |
Note: | Reproducció del document publicat a: http://dx.doi.org/10.1090/S0002-9947-09-04739-4 |
It is part of: | Transactions of the American Mathematical Society, 2009, vol. 361, num. 10, p. 5555-5574 |
URI: | http://hdl.handle.net/2445/95822 |
Related resource: | http://dx.doi.org/10.1090/S0002-9947-09-04739-4 |
ISSN: | 0002-9947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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