# On boundedness properties of certain maximal operators

Colloquium Mathematicae (1995)

- Volume: 68, Issue: 1, page 141-148
- ISSN: 0010-1354

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topMenárguez, M.. "On boundedness properties of certain maximal operators." Colloquium Mathematicae 68.1 (1995): 141-148. <http://eudml.org/doc/210286>.

@article{Menárguez1995,

abstract = {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.},

author = {Menárguez, M.},

journal = {Colloquium Mathematicae},

keywords = {weak type (1,1) boundedness; maximal operators; maximal operator of Hardy-Littlewood; Dirac delta functions},

language = {eng},

number = {1},

pages = {141-148},

title = {On boundedness properties of certain maximal operators},

url = {http://eudml.org/doc/210286},

volume = {68},

year = {1995},

}

TY - JOUR

AU - Menárguez, M.

TI - On boundedness properties of certain maximal operators

JO - Colloquium Mathematicae

PY - 1995

VL - 68

IS - 1

SP - 141

EP - 148

AB - 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.

LA - eng

KW - weak type (1,1) boundedness; maximal operators; maximal operator of Hardy-Littlewood; Dirac delta functions

UR - http://eudml.org/doc/210286

ER -

## References

top- [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.
- [2] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. Zbl0222.26019
- [3] M. de Guzmán, Real Variable Methods in Fourier Analysis, North-Holland Math. Stud. 46, North-Holland, 1981. Zbl0449.42001
- [4] M. T. Menárguez, Discrete methods for weak type inequalities for maximal operators defined on weighted spaces, preprint.
- [5] M. T. Menárguez and F. Soria, Weak type inequalities for maximal convolution operators, Rend. Circ. Mat. Palermo 41 (1992), 342-352. Zbl0770.42013
- [6] F. J. Ruiz and J. L. Torrea, Weighted norm inequalities for a general maximal operator, Ark. Mat. 26 (1986), 327-340. Zbl0666.42015
- [7] F. J. Ruiz and J. L. Torrea, Weighted and vector-valued inequalities for potential operators, Trans. Amer. Math. Soc. 295 (1986), 213-232. Zbl0594.42014
- [8] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, preprint. Zbl0842.42009

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