We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies a weak type 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 . 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.
Keywords: covering lemmas, maximal functions
Mot clés : lemmes de recouvrement, fonctions maximales
@article{AIF_2005__55_5_1439_0, author = {Stokolos, Alexander}, title = {Zygmund's program: some partial solutions}, journal = {Annales de l'Institut Fourier}, pages = {1439--1453}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {55}, number = {5}, year = {2005}, doi = {10.5802/aif.2129}, mrnumber = {2172270}, zbl = {1080.42019}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2129/} }
TY - JOUR AU - Stokolos, Alexander TI - Zygmund's program: some partial solutions JO - Annales de l'Institut Fourier PY - 2005 SP - 1439 EP - 1453 VL - 55 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2129/ DO - 10.5802/aif.2129 LA - en ID - AIF_2005__55_5_1439_0 ER -
%0 Journal Article %A Stokolos, Alexander %T Zygmund's program: some partial solutions %J Annales de l'Institut Fourier %D 2005 %P 1439-1453 %V 55 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2129/ %R 10.5802/aif.2129 %G en %F 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://archive.numdam.org/articles/10.5802/aif.2129/
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