On boundedness properties of certain maximal operators

M. Menárguez

Colloquium Mathematicae (1995)

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

Abstract

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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.

How to cite

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Menárguez, 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

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  1. [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. [2] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. Zbl0222.26019
  3. [3] M. de Guzmán, Real Variable Methods in Fourier Analysis, North-Holland Math. Stud. 46, North-Holland, 1981. Zbl0449.42001
  4. [4] M. T. Menárguez, Discrete methods for weak type inequalities for maximal operators defined on weighted spaces, preprint. 
  5. [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. [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. [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. [8] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, preprint. Zbl0842.42009

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