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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Baldomero Rubio (1978)
Collectanea Mathematica
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Baldomero Rubio (1975)
Collectanea Mathematica
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Alexander Stokolos (2005)
Annales de l’institut Fourier
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We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.
Terasawa, Yutaka (2006)
Journal of Inequalities and Applications [electronic only]
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Ireneo Alonso (1977)
Studia Mathematica
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Luis Caffarelli, Calixto Calderón (1974)
Studia Mathematica
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Björn Jawerth, Alberto Torchinsky (1984)
Studia Mathematica
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M. Menárguez (1995)
Colloquium Mathematicae
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It is known that the weak type (1,1) for the Hardy-Littlewood maximal operator can be obtained from the weak type (1,1) over Dirac deltas. This theorem is due to M. de Guzmán. In this paper, we develop a technique that allows us to prove such a theorem for operators and measure spaces in which Guzmán's technique cannot be used.