On boundedness properties of certain maximal operators
Menárguez, M.
Colloquium Mathematicae, Tome 68 (1995), p. 141-148 / Harvested from The Polish Digital Mathematics Library

It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.

Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:210286
@article{bwmeta1.element.bwnjournal-article-cmv68i1p141bwm,
     author = {M. Men\'arguez},
     title = {On boundedness properties of certain maximal operators},
     journal = {Colloquium Mathematicae},
     volume = {68},
     year = {1995},
     pages = {141-148},
     zbl = {0822.42012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p141bwm}
}
Menárguez, M. On boundedness properties of certain maximal operators. Colloquium Mathematicae, Tome 68 (1995) pp. 141-148. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p141bwm/

[000] [1] R. Coifman, Y. Meyer et E. M. Stein, Un nouvel espace fonctionnel adapté à l'étude des opérateurs définis par des intégrales singulières, in: Lecture Notes in Math. 992, Springer, 1983, 1-15.

[001] [2] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. | Zbl 0222.26019

[002] [3] M. de Guzmán, Real Variable Methods in Fourier Analysis, North-Holland Math. Stud. 46, North-Holland, 1981. | Zbl 0449.42001

[003] [4] M. T. Menárguez, Discrete methods for weak type inequalities for maximal operators defined on weighted spaces, preprint.

[004] [5] M. T. Menárguez and F. Soria, Weak type inequalities for maximal convolution operators, Rend. Circ. Mat. Palermo 41 (1992), 342-352. | Zbl 0770.42013

[005] [6] F. J. Ruiz and J. L. Torrea, Weighted norm inequalities for a general maximal operator, Ark. Mat. 26 (1986), 327-340. | Zbl 0666.42015

[006] [7] F. J. Ruiz and J. L. Torrea, Weighted and vector-valued inequalities for potential operators, Trans. Amer. Math. Soc. 295 (1986), 213-232. | Zbl 0594.42014

[007] [8] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, preprint. | Zbl 0842.42009