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A remark on the centered \(n\)-dimensional Hardy-Littlewood maximal function. (English) Zbl 1037.42021

Summary: We study the behaviour of the \(n\)-dimensional centered Hardy-Littlewood maximal operator associated to the family of cubes with sides parallel to the axes, improving the previously known lower bounds for the best constants \(c_n\) that appear in the weak type \((1,1)\) inequalities.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
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References:

[1] J. M. Aldaz: Remarks on the Hardy-Littlewood maximal function. Proc. Roy. Soc. Edinburgh Sect. A 128A (1998), 1-9. · Zbl 0892.42010 · doi:10.1017/S0308210500027116
[2] D. A. Brannan and W. K. Hayman: Research problems in complex analysis. Bull. London Math. Soc. 21 (1989), 1-35. · Zbl 0695.30001 · doi:10.1112/blms/21.1.1
[3] Ron Dror, Suman Ganguli, and Robert S. Strichartz: A search for best constants in the Hardy-Littlewood Maximal Theorem. J. Fourier Anal. Appl. 2 (1996), 473-486. · Zbl 1055.42502 · doi:10.1007/s00041-001-4039-y
[4] M. de Guzmán: Differentiation of Integrals in \(\mathbb{R}^n\). Lecture Notes in Math. (481), Springer-Verlag, 1975.
[5] M. Trinidad Menarguez: Tecnicas de discretización en análisis armónico para el estudio de acotaciones debiles de operadores maximales e integrales singulares. Ph. D. Thesis, Universidad Complutense de Madrid, 1990.
[6] M. Trinidad Menarguez and F. Soria: Weak type \((1,1)\) inequalities for maximal convolution operators. Rend. Circ. Mat. Palermo XLI (1992), 342-352. · Zbl 0770.42013 · doi:10.1007/BF02848939
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