Transactions of the American Mathematical Society

Author(s): Antonios D. Melas
Journal: Trans. Amer. Math. Soc. 354 (2002), 3263-3273.
MSC (2000): Primary 42B25
Posted: February 20, 2002
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Abstract: We will study the centered Hardy-Littlewood maximal operator acting on positive linear combinations of Dirac deltas. We will use this to obtain improvements in both the lower and upper bounds or the best constant

in the $L^{1}\rightarrow$ weak $L^{1}$ inequality for this operator. In fact we will show that $\frac{11+\sqrt{61}}{12}=1.5675208...\leq C\leq\frac{5} {3}=1.66...$ .

1.: J.M.Aldaz. Remarks on the Hardy-Littlewood maximal function, Proc. of the Royal Society of Edinburgh 128A (1998), no.1, 1-9. MR 99b:42020
2.: D.A.Brannan, W.K. Hayman. Research problems in complex analysis, Bull. London Math. Soc. 21 (1989), 1-35. MR 89m:30001
3.: A.Bernal. A note on the one-dimensional maximal function, Proc. of the Royal Society of Edinburgh 111A (1989), 325-328. MR 90i:28010
4.: H.Carlsson. A new proof of the Hardy Littlewood maximal theorem, Bull. London Math. Soc. 16 (1984), 595-596. MR 86g:42024
5.: A.M.Garsia. Topics in almost everywhere convergence, Markkham Publishing Company, Chicago, 1970. MR 41:5869
6.: L.Grafakos, S.Montgomery-Smith. Best constants for uncentered maximal functions, Bull. London Math. Soc. 29 (1997), no.1, 60-64. MR 98b:42031
7.: M. de Guzmán. Real variable methods in Fourier analysis, North-Holland Mathematical Studies 46. Notas de Mathemática (75), 1981. MR 83j:42019
8.: J. Manfredi, F. Soria. On a dynamical system relared to estimating the best constant in an inequality of Hardy and Littlewood, unpublished manuscript.
9.: M.Trinidad Menarguez, F.Soria. Weak type (1,1) inequalities of maximal convolution operators, Rendiconti del Circolo Mathematico di Palermo (2) 41 (1992), 342-352. MR 94i:42025
10.: D.Termini, C.Vitanza. Weighted estimates for the Hardy-Littlewood maximal operator and Dirac deltas, Bull. London Math. Soc. 22 (1990), 367-374. MR 91f:42018

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