BIBCYT Autor: Alejandría BE 7.0.7b0

Autor: =Barza, Sorina

Sólo un registro cumplió la condición especificada en la base de información BIBCYT.

Autor:	Barza, Sorina ; Kolyada, Viktor ; Soria , Javier
Título:	Sharp constants related to the triangle inequality in Lorentz spaces
Páginas/Colación:	pp. 5555-5574.
Fecha:	October 2009

Transactions of the American Mathematical Society Vol. 361, no.10 October 2009

Información de existencia

Palabras Claves:

EQUIVALENT NORMS,

LEVEL FUNCTION,

LORENTZ SPACES

Resumen
First cohomology groups of finite groups with nontrivial irreducible coefficients have been useful in several geometric and arithmetic contexts, including Wiles's famous paper (1995)

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 .

UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno

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