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.
Original language | English |
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Pages (from-to) | 1439-1453 |
Number of pages | 15 |
Journal | Annales de l'Institut Fourier |
Volume | 55 |
Issue number | 5 |
DOIs | |
State | Published - 2005 |
Scopus Subject Areas
- Algebra and Number Theory
- Geometry and Topology
Keywords
- Covering lemmas
- Maximal functions