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Original Articles

On compactness of the ∂̄-Neumann operator on Hartogs domains

Pages 245-255 | Received 11 Aug 2018, Accepted 31 Dec 2018, Published online: 06 May 2019

References

  • Hörmander L. L2 estimates and existence theorems for the ∂¯ operator. Acta Math. 1965;113:89–152. doi: 10.1007/BF02391775
  • Kohn JJ, Nirenberg L. Non-coercive boundary value problems. Comm Pure Appl Math. 1965;18:443–492. doi: 10.1002/cpa.3160180305
  • Boas HP, Straube EJ Global regularity of the ∂¯-Neumann problem: a survey of the L2-Sobolev theory. In: Several complex variables. Berkeley, CA; 1995–1996. p. 79–111. Math. Sci. Res. Inst. Publ., 37. Cambridge: Cambridge Univ. Press; 1999.
  • Catlin D Global regularity of the ∂¯-Neumann problem. In: Complex analysis of several variables. Madison; 1982. Proc Sympos Pure Math 41, Amer Math Soc, Providence; 1984. p. 39–49.
  • Straube EJ. Plurisubharmonic function and subellipticity of the ∂¯-Neumann problem on non-smooth domains. Math Res Lett. 1997;4:459–467. doi: 10.4310/MRL.1997.v4.n4.a2
  • Fu S, Straube EJ. Compactness of the ∂¯-Neumann operator on convex domains. J Funct Anal. 1998;159. doi: 10.1006/jfan.1998.3317
  • Christ M, Fu S. Compactness in the ∂¯-Neumann problem, maganetic Schrödinger operators, and the Aharonov-Bohm effect. Adv Math. 2005;197:1–40. doi: 10.1016/j.aim.2004.08.015
  • Fu S, Straube EJ. Semi-classical analysis of Schrödinger operators and compactness in the ∂¯-Neumann problem. J Math Anal Apple. 2002;271:267–282; Correction in ibid 2003;208:195–196. doi: 10.1016/S0022-247X(02)00086-0
  • Çelik M, Şahutoğlu S. Compactness of the ∂¯-Neumann operator and commutators of the Bergman projection with continuous functions. J Math Anal Appl. 2014;409(1):393–398. doi: 10.1016/j.jmaa.2013.07.015
  • Şahutoğlu S, Zeytuncu YE. On compactness of Hankel and the ∂¯-Neumann operators on Hartogs domains in C2. J Geom Anal. 2017;27:1274–1285. doi: 10.1007/s12220-016-9718-7
  • Sibony N. Une classe de domaines psedoconvexes. Duke Math J. 1987;55:299–319. doi: 10.1215/S0012-7094-87-05516-5
  • Fuglede B. The Dirichlet Laplacian on finely open sets. Potential Anal. 1999;10:91–101. doi: 10.1023/A:1008630909423
  • Straube EJ Lectures on the L2-Sobolev theory of the ∂¯-Neumann problem. ESI Lectures in Mathematics and Physics. Zrich: European Mathematical Society (EMS); 2010. viii+206 pp. ISBN: 978-3-03719-076-0.
  • Fu S, Straube EJ Compactness of the ∂¯-Neumann operator. In complex analysis and geometry. Columbus; 1999. Ohio State Univ Math Res Inst Publ 9. Berlin: Walter de Gruyter; 2001. p. 141–160.
  • Chen S-C, Shaw M-C Partial differential equations in several complex variables. AMS/IP Studies in Advanced Mathematics, vol.19. RI: International Press, Boston, MA: American Mathematical Society, Providence; 2001.
  • Narasimhan R, Nievergelt Y. Complex analysis in one variable. 2nd ed. Boston: Brikhuser; 2001.

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