In this paper we prove an exponential covering lemma implying the three dimensional case of a well-known conjecture formulated by A. Zygmund circa 1935 and solved by A. Córdoba in 1978. Our approach avoids a subtle argument involving the power series of the exponential function.
Dans cet article, on démontre un lemme de recouvrement exponentiel impliquant le cas tridimensionnel d’une conjecture bien connue formulée par A. Zygmund circa 1935 et prouvée par A. Córdoba en 1978. Notre approche évite un argument subtil qui fati appel à la série entière de la fonction exponentielle.
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Keywords: Maximal functions, Differentiation theorem, Covering lemma.
Mot clés : Fonction maximalz, théorème de différentiation, lemme de recouvrement.
Martínez, Ángel D. 1
@article{AIF_2023__73_2_559_0, author = {Mart{\'\i}nez, \'Angel D.}, title = {C\'ordoba{\textquoteright}s differentiation theorem: revisited}, journal = {Annales de l'Institut Fourier}, pages = {559--565}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {73}, number = {2}, year = {2023}, doi = {10.5802/aif.3535}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3535/} }
TY - JOUR AU - Martínez, Ángel D. TI - Córdoba’s differentiation theorem: revisited JO - Annales de l'Institut Fourier PY - 2023 SP - 559 EP - 565 VL - 73 IS - 2 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3535/ DO - 10.5802/aif.3535 LA - en ID - AIF_2023__73_2_559_0 ER -
%0 Journal Article %A Martínez, Ángel D. %T Córdoba’s differentiation theorem: revisited %J Annales de l'Institut Fourier %D 2023 %P 559-565 %V 73 %N 2 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3535/ %R 10.5802/aif.3535 %G en %F AIF_2023__73_2_559_0
Martínez, Ángel D. Córdoba’s differentiation theorem: revisited. Annales de l'Institut Fourier, Volume 73 (2023) no. 2, pp. 559-565. doi : 10.5802/aif.3535. https://aif.centre-mersenne.org/articles/10.5802/aif.3535/
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