Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0655.47025
Colzani, Leonardo
Translation invariant operators on Lorentz spaces. (English)
[J] Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 14, No.2, 257-276 (1987). ISSN 0391-173X

The main result is as follows: Let $\Omega$ be a locally compact non compact group, equipped with left Haar measure, and let $0<p<+\infty$ and $0<q\le +\infty$. Then every left or right translation invariant linear operator that maps the Lorentz space $L\sp{p,q}(\Omega)$ into $L\sp{p,q}(\Omega)$ continuously, also maps $L\sp p(\Omega)$ into $L\sp p(\Omega)$. Also, the author gives a complete characterization of the bounded left or right translation invariant operators on $L\sp{p,q}(\Omega)$, when $0<p<1$, $0<q\le +\infty$, and $\Omega$ is any locally compact, not necessarily non compact, group. Finally, he improves a result of {\it E. M. Stein}, {\it M. H. Taibleson} and {\it G. Weiss} [Suppl. Rend. Circ. Mat. Palermo II. Ser. 1, 81-97 (1981; Zbl 0503.42018)] on the Bochner-Riesz means involving the Hardy-Lorentz space. See also {\it A. M. Shtejnberg} [Funct. Anal. Appl. 20, 166-168 (1986; Zbl 0605.47033)].
[Lee Peng-Yee]

MSC 2000:: *47B38 Operators on function spaces
46E30 Spaces of measurable functions
42B15 Multipliers, several variables

Keywords: locally compact non compact group, equipped with left Haar measure; right translation invariant linear operator; Lorentz space; Bochner-Riesz means; Hardy-Lorentz space

Citations: Zbl 0503.42018; Zbl 0605.47033

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]