# A sharp estimate for the Hardy-Littlewood maximal function

Loukas Grafakos; Stephen Montgomery-Smith; Olexei Motrunich

Studia Mathematica (1999)

- Volume: 134, Issue: 1, page 57-67
- ISSN: 0039-3223

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topGrafakos, Loukas, Montgomery-Smith, Stephen, and Motrunich, Olexei. "A sharp estimate for the Hardy-Littlewood maximal function." Studia Mathematica 134.1 (1999): 57-67. <http://eudml.org/doc/216622>.

@article{Grafakos1999,

abstract = {The best constant in the usual $L^p$ norm inequality for the centered Hardy-Littlewood maximal function on $ℝ^1$ is obtained for the class of all “peak-shaped” functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.},

author = {Grafakos, Loukas, Montgomery-Smith, Stephen, Motrunich, Olexei},

journal = {Studia Mathematica},

keywords = {peak-shaped function; Hardy-Littlewood maximal function; best constant},

language = {eng},

number = {1},

pages = {57-67},

title = {A sharp estimate for the Hardy-Littlewood maximal function},

url = {http://eudml.org/doc/216622},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Grafakos, Loukas

AU - Montgomery-Smith, Stephen

AU - Motrunich, Olexei

TI - A sharp estimate for the Hardy-Littlewood maximal function

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 1

SP - 57

EP - 67

AB - The best constant in the usual $L^p$ norm inequality for the centered Hardy-Littlewood maximal function on $ℝ^1$ is obtained for the class of all “peak-shaped” functions. A function on the line is called peak-shaped if it is positive and convex except at one point. The techniques we use include variational methods.

LA - eng

KW - peak-shaped function; Hardy-Littlewood maximal function; best constant

UR - http://eudml.org/doc/216622

ER -

## References

top- [Al] J. M. Aldaz, Remarks on the Hardy-Littlewood maximal function, Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 1-9.
- [Ba] J. Barrionuevo, personal comunication.
- [Br] U. Brechtken-Manderscheid, Introduction to the Calculus of Variations, Chapman & Hall, London, 1991.
- [CG] M. Christ and L. Grafakos, Best constants for two nonconvolution inequalities, Proc. Amer. Math. Soc. 123 (1995), 1687-1693. Zbl0830.42009
- [DGS] R. Dror, S. Ganguli and R. Strichartz, A search for best constants in the Hardy-Littlewood maximal theorem, J. Fourier Anal. Appl. 2 (1996), 473-486. Zbl1055.42502
- [GM] L. Grafakos and S. Montgomery-Smith, Best constants for uncentered maximal functions, Bull. London Math. Soc. 29 (1997), 60-64. Zbl0865.42020

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