A remark on weighted inequalities for general maximal operators

Pérez, C.

doi:10.1090/S0002-9939-1993-1107275-0

A remark on weighted inequalities for general maximal operators
HTML articles powered by AMS MathViewer

by C. Pérez PDF

Proc. Amer. Math. Soc. 119 (1993), 1121-1126 Request permission

Abstract:

Let $1 < p < \infty$, and let $w,\;v$ be two nonnegative functions. We give a sufficient condition on $w,\;v$ for which the general maximal operator ${M_\mathcal {B}}$ is bounded from ${L^p}(v)$ into ${L^p}(w)$. Our condition is stronger but closely related to the ${A_{p,\mathcal {B}}}$ condition for two weights.

References

Antonio Cordoba, On the Vitali covering properties of a differentiation basis, Studia Math. 57 (1976), no. 1, 91–95. MR 419714, DOI 10.4064/sm-57-1-91-95
José García-Cuerva and José L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985. Notas de Matemática [Mathematical Notes], 104. MR 807149
R. A. Hunt, D. S. Kurtz, and C. J. Neugebauer, A note on the equivalence of $A_{p}$ and Sawyer’s condition for equal weights, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 156–158. MR 730066
Björn Jawerth, Weighted inequalities for maximal operators: linearization, localization and factorization, Amer. J. Math. 108 (1986), no. 2, 361–414. MR 833361, DOI 10.2307/2374677
Björn Jawerth and Alberto Torchinsky, The strong maximal function with respect to measures, Studia Math. 80 (1984), no. 3, 261–285. MR 783994, DOI 10.4064/sm-80-3-261-285

Harmonic analysis on the bidisc

Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207–226. MR 293384, DOI 10.1090/S0002-9947-1972-0293384-6
C. J. Neugebauer, Inserting $A_{p}$-weights, Proc. Amer. Math. Soc. 87 (1983), no. 4, 644–648. MR 687633, DOI 10.1090/S0002-9939-1983-0687633-2

Weighted norm inequalities for general maximal operators

34

On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted

spaces with different weights

Eric T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), no. 1, 1–11. MR 676801, DOI 10.4064/sm-75-1-1-11
Eric T. Sawyer, Weighted norm inequalities for fractional maximal operators, 1980 Seminar on Harmonic Analysis (Montreal, Que., 1980) CMS Conf. Proc., vol. 1, Amer. Math. Soc., Providence, R.I., 1981, pp. 283–309. MR 670111