Displaying similar documents to “An inequality for the Hardy-Littlewood maximal operator with respect to a product of differentiation bases”

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.

Weighted norm inequalities for general maximal operators.

Carlos Pérez Moreno (1991)

Publicacions Matemàtiques

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The main purpose of this paper is to use some of the results and techniques in [9] to further investigate weighted norm inequalities for Hardy-Littlewood type maximal operators.

Weighted inequalities and the shape of approach regions

José García, Javier Soria (1999)

Studia Mathematica

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We characterize geometric properties of a family of approach regions by means of analytic properties of the class of weights related to the boundedness of the maximal operator associated with this family.