On boundedness properties of certain maximal operators

• Autorzy: M. Trinidad Menárguez
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1995
• Tom: 68
• Numer: 1
• Strony: 141-148

Daty

wydano

1995

otrzymano

1993-10-22

poprawiono

1994-01-05

poprawiono

1994-08-10

Twórcy

autor

M. Trinidad Menárguez

• Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain

Bibliografia

• [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.
• [3] M. de Guzmán, Real Variable Methods in Fourier Analysis, North-Holland Math. Stud. 46, North-Holland, 1981.
• [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.
• [6] F. J. Ruiz and J. L. Torrea, Weighted norm inequalities for a general maximal operator, Ark. Mat. 26 (1986), 327-340.
• [7] F. J. Ruiz and J. L. Torrea, Weighted and vector-valued inequalities for potential operators, Trans. Amer. Math. Soc. 295 (1986), 213-232.
• [8] A. Sánchez-Colomer and J. Soria, Weighted norm inequalities for general maximal operators and approach regions, preprint.