A remark on the centered n -dimensional Hardy-Littlewood maximal function

J. M. Aldaz

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 1, page 103-112
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Aldaz, J. M.. "A remark on the centered $n$-dimensional Hardy-Littlewood maximal function." Czechoslovak Mathematical Journal 50.1 (2000): 103-112. <http://eudml.org/doc/30547>.

@article{Aldaz2000,
abstract = {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.},
author = {Aldaz, J. M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Hardy-Littlewood maximal function; centered Hardy-Littlewood maximal function; weak type inequalities},
language = {eng},
number = {1},
pages = {103-112},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on the centered $n$-dimensional Hardy-Littlewood maximal function},
url = {http://eudml.org/doc/30547},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Aldaz, J. M.
TI - A remark on the centered $n$-dimensional Hardy-Littlewood maximal function
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 1
SP - 103
EP - 112
AB - 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.
LA - eng
KW - Hardy-Littlewood maximal function; centered Hardy-Littlewood maximal function; weak type inequalities
UR - http://eudml.org/doc/30547
ER -

References

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  1. Remarks on the Hardy-Littlewood maximal function, Proc. Roy. Soc. Edinburgh Sect. A 128A (1998), 1–9. (1998) Zbl0892.42010MR1606325
  2. 10.1112/blms/21.1.1, Bull. London Math. Soc. 21 (1989), 1–35. (1989) MR0967787DOI10.1112/blms/21.1.1
  3. 10.1007/s00041-001-4039-y, J. Fourier Anal. Appl. 2 (1996), 473–486. (1996) MR1412064DOI10.1007/s00041-001-4039-y
  4. Differentiation of Integrals in ℝ n , Lecture Notes in Math. (481), Springer-Verlag, 1975. (1975) MR0457661
  5. 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. (1990) 
  6. Weak type ( 1 , 1 ) inequalities for maximal convolution operators, Rend. Circ. Mat. Palermo XLI (1992), 342–352. (1992) MR1230582

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