We define weak , a generalization of on bounded domains in a Stein manifold that suffices to prove closed range of . Under the hypothesis of weak , we also show (i) that harmonic -forms are trivial and (ii) if satisfies weak and weak , then has closed range on -forms on . We provide examples to show that our condition contains examples that are excluded from -pseudoconvexity and the authors’ previous notion of weak .
Nous définissons faible, une généralisation de sur les domaines bornés dans une variété de Stein qui suffit à prouver que l’image de est fermée. Sous l’hypothèse d’une faible, nous montrons également que (i) les -formes harmoniques sont triviales et (ii) si satisfait une faible et une faible, alors a une image fermée sur les -formes sur . Nous fournissons des exemples pour montrer que notre condition contient des exemples qui sont exclus de la -pseudoconvexité et la notion précédente des auteurs de faible.
Accepted:
Published online:
Classification: 32W05, 32W10, 32Q28, 35N15
Keywords: Stein manifold, , tangential Cauchy-Riemann operator, closed range, -Neumann, weak , -pseudoconvexity
@article{AIF_2015__65_4_1711_0, author = {Harrington, Phillip S. and Raich, Andrew S.}, title = {Closed {Range} for $\bar{\partial }$ and $\bar{\partial }_b$ on {Bounded} {Hypersurfaces} in {Stein} {Manifolds}}, journal = {Annales de l'Institut Fourier}, pages = {1711--1754}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {65}, number = {4}, year = {2015}, doi = {10.5802/aif.2972}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2972/} }
TY - JOUR TI - Closed Range for $\bar{\partial }$ and $\bar{\partial }_b$ on Bounded Hypersurfaces in Stein Manifolds JO - Annales de l'Institut Fourier PY - 2015 DA - 2015/// SP - 1711 EP - 1754 VL - 65 IS - 4 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2972/ UR - https://doi.org/10.5802/aif.2972 DO - 10.5802/aif.2972 LA - en ID - AIF_2015__65_4_1711_0 ER -
%0 Journal Article %T Closed Range for $\bar{\partial }$ and $\bar{\partial }_b$ on Bounded Hypersurfaces in Stein Manifolds %J Annales de l'Institut Fourier %D 2015 %P 1711-1754 %V 65 %N 4 %I Association des Annales de l’institut Fourier %U https://doi.org/10.5802/aif.2972 %R 10.5802/aif.2972 %G en %F AIF_2015__65_4_1711_0
Harrington, Phillip S.; Raich, Andrew S. Closed Range for $\bar{\partial }$ and $\bar{\partial }_b$ on Bounded Hypersurfaces in Stein Manifolds. Annales de l'Institut Fourier, Volume 65 (2015) no. 4, pp. 1711-1754. doi : 10.5802/aif.2972. https://aif.centre-mersenne.org/articles/10.5802/aif.2972/
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