Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-18T03:20:29.082Z Has data issue: false hasContentIssue false
  • English
  • Français

Remarks on the Hardy–Littlewood maximal function

Published online by Cambridge University Press:  14 November 2011

J. M. Aldaz
J. M. Aldaz
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain E-mail: aldaz@ccuam3.sdi.uam.es
Get access Rights & Permissions [Opens in a new window]

Extract

We answer questions of A. Carbery, M. Trinidad Menárguez and F. Soria by proving, firstly, that for the centred Hardy–Littlewood maximal function on the real line, the best constant C for the weak type (1, 1) inequality is strictly larger than 3/2, and secondly, that C is strictly less than 2 (known to be the best constant in the noncentred case).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 1 , 1998 , pp. 1 - 9
Copyright
Copyright © Royal Society of Edinburgh 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Bernal, A.. A note on the one-dimensional maximal function. Proc. Roy. Soc. Edinburgh Sect. A 111 (1989), 325–8.CrossRefGoogle Scholar
2Brannan, D. A. and Hayman, W. K.. Research problems in complex analysis. Bull. London Math. Soc. 21 (1989), 1–35.CrossRefGoogle Scholar
3Carlsson, H.. A new proof of the Hardy–Littlewood maximal theorem. Bull. London Math. Soc. 16 (1984), 595–6.CrossRefGoogle Scholar
4Garsia, A. M.. Topics in almost everywhere convergence (Chicago: Markham, 1970).Google Scholar
5Guzman, M. de. Real Variable Methods in Fourier Analysis, North-Holland Mathematical Studies 46, Notas de Matematica (75), 1981.Google Scholar
6Menarguez, M. Trinidad and Soria, F.. Weak type (1,1) inequality of maximal convolution operators. Rend. Circ. Mat. Palermo XLI (1992), 342–52.CrossRefGoogle Scholar
7Stein, E. M. and Stromberg, J. O.. Behaviour of maximal functions in ℝn for large n. Ark. Mat. 21 (1983), 259–69.Google Scholar
8Termini, D. and Vitanza, C.. Weighted estimates for the Hardy–Littlewood maximal operator and Dirac deltas. Bull. London Math. Soc. 22 (1990), 367–74.Google Scholar