Weighted Sobolev spaces in complex ellipsoids

Joaquín M. Ortega; Joan Fàbrega

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1996)

  • Volume: 23, Issue: 2, page 325-362
  • ISSN: 0391-173X

How to cite


Ortega, Joaquín M., and Fàbrega, Joan. "Weighted Sobolev spaces in complex ellipsoids." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 23.2 (1996): 325-362. <http://eudml.org/doc/84233>.

author = {Ortega, Joaquín M., Fàbrega, Joan},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {division problem; -equation; weighted Sobolev spaces; complex ellipsoids; regularity; extension problems},
language = {eng},
number = {2},
pages = {325-362},
publisher = {Scuola normale superiore},
title = {Weighted Sobolev spaces in complex ellipsoids},
url = {http://eudml.org/doc/84233},
volume = {23},
year = {1996},

AU - Ortega, Joaquín M.
AU - Fàbrega, Joan
TI - Weighted Sobolev spaces in complex ellipsoids
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1996
PB - Scuola normale superiore
VL - 23
IS - 2
SP - 325
EP - 362
LA - eng
KW - division problem; -equation; weighted Sobolev spaces; complex ellipsoids; regularity; extension problems
UR - http://eudml.org/doc/84233
ER -


  1. [AD1] K. Adachi, Extending bounded holomorphic functions from certain subvarieties of a weakly pseudoconvex domain, Pacific J. Math.110 (1984), 9-19. Zbl0477.32013MR722733
  2. [AD 2] K. Adachi, Continuation of bounded holomorphic functions from certain subvarieties to weakly pseudoconvex domains, Pacific J. Math.130 (1987), 1-8. Zbl0589.32025MR910650
  3. [AD 3] K. Adachi, Extending HP functions from subvarieties to real ellipsoids, Trans. Amer. Math. Soc.317 (1990), 351-359. Zbl0687.32007MR946214
  4. [AM] E. Amar, Cohomologie complexe et applications, J. London Math. Soc.29 (1984),127-140. Zbl0583.32033MR734998
  5. [BEA] F. Beatrous, Estimates for Derivatives of Holomorphic Functions in Pseudoconvex Domains, Math. Z.191 (1986), 91-116. Zbl0596.32005MR812605
  6. [BER-AN] B. Berndtsson - M. Andersson, Henkin-Ramirez Formulas with Weight Factors, Ann. Inst. Fourier (Grenoble) 32 (1983), 91-110. Zbl0466.32001MR688022
  7. [BER] B. Berndtsson, A formula for Interpolation and Division in Cn, Math. Ann.263 (1983), 399-412. Zbl0499.32013MR707239
  8. [B-CHA] A. Bonomi - PH. Crarpentier, Solutions de l'equation ∂ et zeros de la classe de Nevalinna dans certains domaines faiblement pseudo-convexes, Ann. Inst. Fourier (Grenoble) 32 (1982), 53-89. Zbl0493.32005
  9. [BO-CU-ZE] P. Bonneau - A. Cumenge - A. Zériahi, Division dans les espaces de Lipschitz de fonction's holomorphes, C.R. Acad. Sci. Paris297 (1983), 517-520. Zbl0576.32025MR735489
  10. [BO-DI] P. Bonneau - K. Diederich, Integral solution operators for the Cauchy-Riemann equations on pseudoconvex domains, Math. Ann.286 (1990), 77-100. Zbl0698.47020MR1032924
  11. [BR-CA] J. Bruna - J. Castillo, Hölder and L P -estimatesfor the ∂-equation in some convex domains with real analytic boundary, Mat. Ann.269 (1984), 527-539. Zbl0533.32010
  12. [BR-OR] J. Bruna - J.M. Ortega, Interpolation by Holomorphic Functions Smooth to the Boundary in the Unit Ball of Cn, Math. Ann.274 (1986), 527-575. Zbl0585.32018MR848501
  13. [CH-NA-ST] D.C. Chang - A. Nagel - E.M. Stein, Estimates for the ∂-Neumann problem in pseudoconvex domains of finite type in C2, Acta Math.169 (1992), 153-228. Zbl0821.32011
  14. [CHE-KR-MA] Z. Chen - S.G. Krantz - D. Ma, Optimal Lp estimates for the ∂-equation in C2, Manuscripta Math.80 (1993), 131-150. Zbl0789.32011
  15. [CU] A. Cumenge, Extension dans les classes de Hardy de fonctions holomorphes et estimations de type "Mesures de Carleson " pour l'equations ∂, Ann. Inst. Fourier (Grenoble) 33 (1983), 59-97. Zbl0487.32011
  16. [DI-FO] K. Diederich - J.E. Fornaess - J. Wiegerinck, Sharp Hölder estimates for ∂ on ellipsoids, Manuscripta Math.56 (1986), 399-417. Zbl0602.32006
  17. [GR-ST] P.C. Greiner - E.M. Stein, Estimates for the ∂-Neumann problem, Princeton University Press, 1977. Zbl0354.35002
  18. [GRE] S. Grellier, Behavior of holomorphic functions in complex tangential directions in a domain offinite type in Cn, Publ. Mat.36 (1992), 251-292. Zbl0758.32004MR1179617
  19. [HE] G.M. Henkin, Continuation of bounded holomorphicfunctionsfrom submanifolds in general position to strictly pseudoconvex domains, Math. USSR-Izv.6 (1972), 536-563. Zbl0255.32008
  20. [HI] M. Hickel, Sur un probleme de division dans l'algebre A∞ (D) d'un ouvert faiblemment pseudoconvexe de (C2, Math. Z.197 (1988), 201-218. Zbl0617.32024
  21. [KE] N. Kerzman, Hölder and Lp estimates for solutions of ∂u = f in strongly pseudoconvex domains, Comm. Pure Appl. Math.24 (1971), 301-379. Zbl0205.38702
  22. [KO] J.J. Kohn, Boundary behavior of ∂ on weakly pseudoconvex manifolds of dimension two, J. Differential Geometry6 (1972), 523-542. Zbl0256.35060
  23. [KO] S.G. Krantz, Optimal Lipschitz and LP regularity for the equation ∂u = f on strongly pseudoconvex domains, Math. Ann.219 (1976), 233-260. Zbl0303.35059
  24. [NA-ST-WA] A. Nagel - E.M. Stein - S. Wainger, Boundary behavior of functions holomorphic in domains offinite type, Proc. Nat. Acad. Sci. U.S.A.78 (1980), 6596-6599. Zbl0517.32002MR634936
  25. [OK] G.O. Okikiolu, Aspects of the Theory of Bounded integral operators in Lpspaces, Academic Press. London - New York, 1971. Zbl0219.44002MR445237
  26. [OR-FA 1] J.M. Ortega - J. Fàbrega, Division and Extension in weighted Bergman-Sobolev spaces, Publ. Mat.36 (1992), 837-859. Zbl0777.32004MR1210023
  27. [OR-FA 2] J.M. Ortega - J. Fàbrega, Mixed-norm spaces and interpolation, Studia Math.109 (1994), 233-254. Zbl0826.32003MR1274011
  28. [OV] N. Ovrelid, Integral representations formulas and L p estimates for the ∂ equation, Math. Scand.29 (1971), 137-160. Zbl0227.35069
  29. [RA] R.M. Range, On Hölder estimates for ∂u = f on weakly pseudoconvex domains, Proceedings of International Conferences. Cortona, Italy 1976- 1977. Scuola Norm. Sup. Pisa (1978), 247-267. Zbl0421.32021

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.