A sharp estimate for the Hardy-Littlewood maximal function

• Autorzy: Loukas Grafakos , Stephen Montgomery-Smith , Olexei Motrunich
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1999
• Tom: 134
• Numer: 1
• Strony: 57-67

Daty

wydano

1999

otrzymano

1998-02-02

poprawiono

1998-06-17

Twórcy

autor

Loukas Grafakos

• Department of Mathematics, University of Missouri, Columbia, Missouri 65211, U.S.A.

autor

Stephen Montgomery-Smith

• Department of Mathematics, University of Missouri Columbia, Missouri 65211, U.S.A.

autor

Olexei Motrunich

• Department of Physics, Princeton University, Princeton, New Jersey 08544, U.S.A.

Bibliografia

• [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.
• [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.
• [GM] L. Grafakos and S. Montgomery-Smith, Best constants for uncentered maximal functions, Bull. London Math. Soc. 29 (1997), 60-64.