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An elementary approach to several results on the Hardy-Littlewood maximal operator.(English)Zbl 1273.42019

Summary: We give new elementary proofs of theorems due to B. Muckenhoupt, B. Jawerth, and S. Buckley. By means of our approach we answer a question raised byJ. Orobitg andC. Pérez [Trans. Am. Math. Soc. 354, No. 5, 2013–2033 (2002;Zbl 0998.42012)].

MSC:

42B25 Maximal functions, Littlewood-Paley theory

Citations:

Zbl 0998.42012

Cite

References:

[1]Stephen M. Buckley, Estimates for operator norms on weighted spaces and reverse Jensen inequalities, Trans. Amer. Math. Soc. 340 (1993), no. 1, 253 – 272. ·Zbl 0795.42011
[2]Michael Christ and Robert Fefferman, A note on weighted norm inequalities for the Hardy-Littlewood maximal operator, Proc. Amer. Math. Soc. 87 (1983), no. 3, 447 – 448. ·Zbl 0502.42017
[3]R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241 – 250. ·Zbl 0291.44007
[4]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. ·Zbl 0578.46046
[5]Miguel de Guzmán, Differentiation of integrals in \?\(^{n}\), Lecture Notes in Mathematics, Vol. 481, Springer-Verlag, Berlin-New York, 1975. With appendices by Antonio Córdoba, and Robert Fefferman, and two by Roberto Moriyón. ·Zbl 0598.28006
[6]R. A. Hunt, D. S. Kurtz, and C. J. Neugebauer, A note on the equivalence of \?_{\?} 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.
[7]Björn Jawerth, Weighted inequalities for maximal operators: linearization, localization and factorization, Amer. J. Math. 108 (1986), no. 2, 361 – 414. ·Zbl 0608.42012 ·doi:10.2307/2374677
[8]Benjamin Muckenhoupt, Weighted norm inequalities for the Hardy maximal function, Trans. Amer. Math. Soc. 165 (1972), 207 – 226. ·Zbl 0236.26016
[9]Joan Orobitg and Carlos Pérez, \?_{\?} weights for nondoubling measures in \?\(^{n}\) and applications, Trans. Amer. Math. Soc. 354 (2002), no. 5, 2013 – 2033. ·Zbl 0998.42012
[10]Eric T. Sawyer, A characterization of a two-weight norm inequality for maximal operators, Studia Math. 75 (1982), no. 1, 1 – 11. ·Zbl 0508.42023
[11]Peter Sjögren, A remark on the maximal function for measures in \?\(^{n}\), Amer. J. Math. 105 (1983), no. 5, 1231 – 1233. ·Zbl 0528.42007 ·doi:10.2307/2374340
[12]Peter Sjögren and Fernando Soria, Sharp estimates for the non-centered maximal operator associated to Gaussian and other radial measures, Adv. Math. 181 (2004), no. 2, 251 – 275. ·Zbl 1040.42019 ·doi:10.1016/S0001-8708(03)00050-1
[13]Ana M. Vargas, On the maximal function for rotation invariant measures in \?\(^{n}\), Studia Math. 110 (1994), no. 1, 9 – 17. ·Zbl 0818.42009
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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