|
Weak-type weights and normable Lorentz spaces
Author(s):
María
J.
Carro;
Alejandro
García
del Amo;
Javier
Soria
Journal:
Proc. Amer. Math. Soc.
124
(1996),
849-857.
MSC (1991):
Primary 42B25, 46E30
MathSciNet review:
1307501
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We show that the Lorentz space  is a Banach space if and only if the Hardy-Littlewood maximal operator  satisfies a certain weak-type estimate. We also consider the case of general measures. Finally, we study some properties of several indices associated to these spaces.
References:
- [AM]
- M.A. Ariño and B. Muckenhoupt, Maximal functions on classical Lorentz spaces and Hardy's inequality with weights for nonincreasing functions, Trans. Amer. Math. Soc. 320 (1990), 727--735. MR 90k:42034
- [BS]
- C. Bennett and R. Sharpley, Interpolation of operators, Academic Press, New York, 1988. MR 89e:46001
- [CS1]
- M.J. Carro and J. Soria, Weighted Lorentz spaces and the Hardy operator, J. Funct. Anal. 112 (1993), 480--494. MR 94f:42025
- [CS2]
- ------, Boundedness of some integral operators, Canad. J. Math. 45 (1993), 1155--1166. MR 95d:47064
- [CS3]
- ------, The Hardy--Littlewood maximal function and weighted Lorentz spaces, J. London Math. Soc. (to appear).
- [GR]
- J. García-Cuerva and J.L. Rubio de Francia, Weighted norm inequalities and related topics, Math. Stud., vol. 116, North-Holland, Amsterdam, 1985. MR 87d:42023
- [GuR]
- M. de Guzmán and B. Rubio, Problemas, conceptos y métodos del análisis matemático I, Ediciones Pirámide, 1990.
- [Hu]
- R.A. Hunt, On
 spaces, Enseign. Math. (2) 12 (1966), 249--276. MR 36:6921 - [KPS]
- S.G. Krein, Ju.I. Petunin, and E.M. Semenov, Interpolation of linear operators, Transl. Math. Monographs, vol. 54, Amer. Math. Soc., Providence, RI, 1982. MR 84j:46013
- [Lo]
- G.G. Lorentz, On the theory of spaces
 , Pacific J. Math. 1 (1951), 411--429. - [Ma]
- L. Maligranda, Indices and interpolation, Dissertationes Math. 234 (1985). MR 87k:46059
- [Ne]
- C.J. Neugebauer, Weighted norm inequalities for averaging operators of monotone functions, Publ. Mat. 35 (1991), 429--447. MR 93m:26042
- [Ra]
- Y. Raynaud, On Lorentz-Sharpley spaces, Israel Math. Conf. Proc. 5 (1992), 207--228. MR 94c:46061
- [Sa]
- E. Sawyer, Boundedness of classical operators on classical Lorentz spaces, Studia Math. 96 (1990), 145--158. MR 91d:26026
- [Sj]
- P. Sjögren, How to recognize a discrete maximal function, Indiana Univ. Math. J. 37 (1988), 891--898. MR 90f:42020
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
42B25, 46E30
Retrieve articles in all Journals with
MSC (1991):
42B25, 46E30
Additional Information:
María
J.
Carro
Affiliation:
Departamento Matemàtica Aplicada i Anàlisi, Universidad de Barcelona, 08071 Barcelona, Spain
Email:
carro@cerber.mat.ub.es
Alejandro
García
del Amo
Affiliation:
Departamento Análisis Matemático, Facultad de Ciencias, Matemáticas, Universidad Complutense, 28040 Madrid, Spain
Address at time of publication:
Departamento Matemática Pura y Aplicada, Facultad de Ciencias, Universidad de Salamanca, 37008 Salamanca, Spain
Email:
garciada@mat.ucm.es
Javier
Soria
Affiliation:
Departamento Matemàtica Aplicada i Anàlisi, Universidad de Barcelona, 08071 Barcelona, Spain
Email:
soria@cerber.mat.ub.es
DOI:
10.1090/S0002-9939-96-03214-5
PII:
S 0002-9939(96)03214-5
Received by editor(s):
September 14, 1994
Additional Notes:
The first and third authors were partially supported by DGICYT PB94--0879. \endgraf The second author was partially supported by DGICYT PB94--0243.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1996,
American Mathematical Society
|
