The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals

Baldomero Rubio

Displaying similar documents to “The property of weak type (p,p) for the Hardy-Littlewood maximal operator and derivation of integrals”

An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases

Miguel de Guzmán (1974)

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The maximal, funtion and derivation of integrals in a space of locally integrable functions.

Baldomero Rubio (1978)

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The hardy-littlewood maximal function and derivation of integrals.

Baldomero Rubio (1975)

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Zygmund's program: some partial solutions

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 $(1, 1)$ 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.

Outer measures and weak type $(1, 1)$ estimates of Hardy-Littlewood maximal operators.

Terasawa, Yutaka (2006)

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A general result on the equivalence between derivation of integrals and weak inequalities for the Hardy-Littlewood maximal operator

Ireneo Alonso (1977)

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Weak type estimates for the Hardy-Littlewood maximal functions

Luis Caffarelli, Calixto Calderón (1974)

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The strong maximal function with respect to measures

Björn Jawerth, Alberto Torchinsky (1984)

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On boundedness properties of certain maximal operators

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.