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Hardy-Littlewood maximal function
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.
[A] J. M. Aldaz: Remarks on the Hardy-Littlewood maximal function. Proc. Roy. Soc. Edinburgh Sect. A 128A (1998), 1–9. MR 1606325 | Zbl 0892.42010
[BH] D. A. Brannan and W. K. Hayman: Research problems in complex analysis. Bull. London Math. Soc. 21 (1989), 1–35. DOI 10.1112/blms/21.1.1 | MR 0967787
[DrGaSt] 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. DOI 10.1007/s00041-001-4039-y | MR 1412064
[Gu] M. de Guzmán: Differentiation of Integrals in $\mathbb{R}^n$. Lecture Notes in Math. (481), Springer-Verlag, 1975. MR 0457661
[M] 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.
[MS] M. Trinidad Menarguez and F. Soria: Weak type $(1,1)$ inequalities for maximal convolution operators. Rend. Circ. Mat. Palermo XLI (1992), 342–352. MR 1230582
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