Zygmund's program: some partial solutions
Annales de l'Institut Fourier, Volume 55 (2005) no. 5, p. 1439-1453
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.
Nous proposons un critère simple pour décider si la fonction maximale associée à une base d’intervalles multidimensionnels, invariante par translation, admet une estimation du type (1,1). Cela nous permet de compléter le programme de Zygmund décrivant les bases d’intervalles multidimensionnels invariantes par translation dans le cas particulier des produits de deux intervalles cubiques. Nous proposons aussi une conjecture qui précise le programme de Zygmund.
DOI : https://doi.org/10.5802/aif.2129
Classification:  42B25
Keywords: covering lemmas, maximal functions
@article{AIF_2005__55_5_1439_0,
     author = {Stokolos, Alexander},
     title = {Zygmund's program: some partial solutions},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {55},
     number = {5},
     year = {2005},
     pages = {1439-1453},
     doi = {10.5802/aif.2129},
     zbl = {1080.42019},
     mrnumber = {2172270},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2005__55_5_1439_0}
}
Stokolos, Alexander. Zygmund's program: some partial solutions. Annales de l'Institut Fourier, Volume 55 (2005) no. 5, pp. 1439-1453. doi : 10.5802/aif.2129. http://www.numdam.org/item/AIF_2005__55_5_1439_0/

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