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Alexander Stokolos
Zygmund's program: some partial solutions
(Programme de Zygmund : quelques solutions partielles)
Annales de l'institut Fourier, 55 no. 5 (2005), p. 1439-1453, doi: 10.5802/aif.2129
Article PDF | Reviews MR 2172270 | Zbl 1080.42019
Class. Math.: 42B25
Keywords: covering lemmas, maximal functions

Résumé - Abstract

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.

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