TY - JOUR
T1 - on the L 2 -dolbeault cohomology of annuli
AU - Chakrabarti, Debraj
AU - Laurent-Thiébaut, Christine
AU - Shaw, Mei Chi
N1 - Funding Information:
The authors gratefully acknowledge the valuable comments and suggestions of Y.-T. Siu on the topic of this paper. The authors are also thankful to the referee for helpful suggestions. Debraj Chakrabarti was partially supported by the Simons Foundation (grant no. 316632), by an Early Career internal grant from Central Michigan University, and also by the NSF (grant no. 1600371). Mei-Chi Shaw was partially supported by a grant from the NSF. All three authors were partially supported by a grant from the AGIR program of Grenoble INP and the Université Joseph Fourier, awarded to Christine Laurent-Thiébaut.
Funding Information:
Debraj Chakrabarti was partially supported by the Simons Foundation (grant no. 316632), by an Early Career internal grant from Central Michigan University, and also by the NSF (grant no. 1600371). Mei-Chi Shaw was partially supported by a grant from the NSF. All three authors were partially supported by a grant from the AGIR program of Grenoble INP and the Université Joseph Fourier, awarded to Christine Laurent-Thiébaut.
Publisher Copyright:
© 2018 Department of Mathematics, Indiana University. All rights reserved.
PY - 2018
Y1 - 2018
N2 - For certain annuli in C n , n á 2, with non-smooth holes, we show that the ∂ s -operator from L 2 functions to L 2 (0, 1)-forms has closed range. The holes admitted include products of pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex domains. As a consequence, we obtain estimates in the Sobolev space W 1 for the ∂ s -equation on the non-smooth domains which are the holes of these annuli.
AB - For certain annuli in C n , n á 2, with non-smooth holes, we show that the ∂ s -operator from L 2 functions to L 2 (0, 1)-forms has closed range. The holes admitted include products of pseudoconvex domains and certain intersections of smoothly bounded pseudoconvex domains. As a consequence, we obtain estimates in the Sobolev space W 1 for the ∂ s -equation on the non-smooth domains which are the holes of these annuli.
UR - http://www.scopus.com/inward/record.url?scp=85064336276&partnerID=8YFLogxK
U2 - 10.1512/iumj.2018.67.7307
DO - 10.1512/iumj.2018.67.7307
M3 - Article
AN - SCOPUS:85064336276
SN - 0022-2518
VL - 67
SP - 831
EP - 857
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 2
ER -