We show that Petermichl's dyadic operator (Petermichl (2000) [8]) is a Calderón–Zygmund-type operator on an adequate metric normal space of homogeneous type. We also compare the maximal operators associated with truncations of the kernel and to the summability of the Haar series.
Nous démontrons que l'opérateur dyadique de Petermichl est un opérateur de type Calderón–Zygmund sur un espace normal métrique de type homogène. Nous comparons les opérateurs maximaux associés aux troncatures du noyau et à la sommabilité de la série de Haar.
Accepted:
Published online:
@article{CRMATH_2018__356_5_509_0,
author = {Aimar, Hugo and G\'omez, Ivana},
title = {On the {Calder\'on{\textendash}Zygmund} structure of {Petermichl's} kernel},
journal = {Comptes Rendus. Math\'ematique},
pages = {509--516},
publisher = {Elsevier},
volume = {356},
number = {5},
year = {2018},
doi = {10.1016/j.crma.2018.04.002},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.crma.2018.04.002/}
}
TY - JOUR AU - Aimar, Hugo AU - Gómez, Ivana TI - On the Calderón–Zygmund structure of Petermichl's kernel JO - Comptes Rendus. Mathématique PY - 2018 SP - 509 EP - 516 VL - 356 IS - 5 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.crma.2018.04.002/ DO - 10.1016/j.crma.2018.04.002 LA - en ID - CRMATH_2018__356_5_509_0 ER -
%0 Journal Article %A Aimar, Hugo %A Gómez, Ivana %T On the Calderón–Zygmund structure of Petermichl's kernel %J Comptes Rendus. Mathématique %D 2018 %P 509-516 %V 356 %N 5 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.crma.2018.04.002/ %R 10.1016/j.crma.2018.04.002 %G en %F CRMATH_2018__356_5_509_0
Aimar, Hugo; Gómez, Ivana. On the Calderón–Zygmund structure of Petermichl's kernel. Comptes Rendus. Mathématique, Volume 356 (2018) no. 5, pp. 509-516. doi : 10.1016/j.crma.2018.04.002. https://www.numdam.org/articles/10.1016/j.crma.2018.04.002/
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Cited by Sources:
☆ This work was supported by CONICET (grant PIP-112-2011010-0877, 2012); ANPCyT-MINCyT (grants PICT-2568, 2012; PICT-3631, 2015); and UNL (grant CAID-50120110100371LI, 2013).
