| Title:
|
A remark on the centered $n$-dimensional Hardy-Littlewood maximal function (English) |
| Author:
|
Aldaz, J. M. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2000 |
| Pages:
|
103-112 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Hardy-Littlewood maximal function |
| MSC:
|
42A99 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 1037.42021 |
| idMR:
|
MR1745465 |
| . |
| Date available:
|
2009-09-24T10:30:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127554 |
| . |
| Reference:
|
[A] J. M. Aldaz: Remarks on the Hardy-Littlewood maximal function.Proc. Roy. Soc. Edinburgh Sect. A 128A (1998), 1–9. Zbl 0892.42010, MR 1606325 |
| Reference:
|
[BH] D. A. Brannan and W. K. Hayman: Research problems in complex analysis.Bull. London Math. Soc. 21 (1989), 1–35. MR 0967787, 10.1112/blms/21.1.1 |
| Reference:
|
[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. MR 1412064, 10.1007/s00041-001-4039-y |
| Reference:
|
[Gu] M. de Guzmán: Differentiation of Integrals in $\mathbb{R}^n$.Lecture Notes in Math. (481), Springer-Verlag, 1975. MR 0457661 |
| Reference:
|
[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. |
| Reference:
|
[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 |
| . |
