An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases
Miguel de Guzmán (1974)
Studia Mathematica
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Miguel de Guzmán (1974)
Studia Mathematica
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Irina Asekritova, Natan Krugljak, Lech Maligranda, Lars-Erik Persson (1997)
Studia Mathematica
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There are given necessary and sufficient conditions on a measure dμ(x)=w(x)dx under which the key estimates for the distribution and rearrangement of the maximal function due to Riesz, Wiener, Herz and Stein are valid. As a consequence, we obtain the equivalence of the Riesz and Wiener inequalities which seems to be new even for the Lebesgue measure. Our main tools are estimates of the distribution of the averaging function f** and a modified version of the Calderón-Zygmund decomposition....
Soulaymane Korry (2001)
Collectanea Mathematica
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H. Länger (1978)
Fundamenta Mathematicae
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Mark Leckband (1987)
Studia Mathematica
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Björn Jawerth, Alberto Torchinsky (1984)
Studia Mathematica
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D. Burkholder, R. Gundy (1972)
Studia Mathematica
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Akihiko Miyachi (1990)
Studia Mathematica
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Baldomero Rubio (1978)
Collectanea Mathematica
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Loukas Grafakos, Stephen Montgomery-Smith, Olexei Motrunich (1999)
Studia Mathematica
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The best constant in the usual norm inequality for the centered Hardy-Littlewood maximal function on 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.
A. M. Stokolos (2006)
Colloquium Mathematicae
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The study of one-dimensional rare maximal functions was started in [4,5]. The main result in [5] was obtained with the help of some general procedure. The goal of the present article is to adapt the procedure (we call it "dyadic crystallization") to the multidimensional setting and to demonstrate that rare maximal functions have properties not better than the Strong Maximal Function.