C k -regularity for the ∂ ¯ -equation on a piecewise smooth union of strictly pseudoconvex domains in ℂ n

Joachim Michel; Alessandro Perotti

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1994)

  • Volume: 21, Issue: 4, page 483-495
  • ISSN: 0391-173X

How to cite

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Michel, Joachim, and Perotti, Alessandro. "$C^k$-regularity for the $\bar{\partial }$-equation on a piecewise smooth union of strictly pseudoconvex domains in $\mathbb {C}^n$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 21.4 (1994): 483-495. <http://eudml.org/doc/84189>.

@article{Michel1994,
author = {Michel, Joachim, Perotti, Alessandro},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Cauchy-Riemann equations; strongly pseudoconvex domains},
language = {eng},
number = {4},
pages = {483-495},
publisher = {Scuola normale superiore},
title = {$C^k$-regularity for the $\bar\{\partial \}$-equation on a piecewise smooth union of strictly pseudoconvex domains in $\mathbb \{C\}^n$},
url = {http://eudml.org/doc/84189},
volume = {21},
year = {1994},
}

TY - JOUR
AU - Michel, Joachim
AU - Perotti, Alessandro
TI - $C^k$-regularity for the $\bar{\partial }$-equation on a piecewise smooth union of strictly pseudoconvex domains in $\mathbb {C}^n$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1994
PB - Scuola normale superiore
VL - 21
IS - 4
SP - 483
EP - 495
LA - eng
KW - Cauchy-Riemann equations; strongly pseudoconvex domains
UR - http://eudml.org/doc/84189
ER -

References

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  1. [1] L.A. Aĭzenberg - Sh.A. Dautov, Differential Forms Orthogonal to Holomorphic Functions or Forms and Their Properties. A.M.S. Providence RI, 1983. Zbl0511.32002MR700397
  2. [2] M. Jambon, L'équation différentielle de Cauchy-Riemann sur une domaine strictement pseudoconvexe. Solutions bornées. Enseign. Math.18 (1972), 304-337. Zbl0255.35075MR330512
  3. [3] I. Lieb - R.M. Range, Lösungoperatoren für den Cauchy-Riemann-Komplex mit Ck-Abschätzungen. Math. Ann., 253 (1980), 145-164. Zbl0441.32007MR597825
  4. [4] J. Michel, Integralformeln in der komplexen Analysis. Bonn. Math. Schr.133 (1981), 1-152. Zbl0504.32002MR630297
  5. [5] J. Michel, Beschränkte Integraloperatoren auf streng q-konvexem Gebieten in Cn. Journal Reine Angew. Math., 351 (1984), 192-215. Zbl0578.32005MR749682
  6. [6] J. Michel, Randregularitdt des ∂-Problems für stückweise streng pseudokonvexe Gebiete in Cn. Math. Ann.280 (1988), 45-68. Zbl0617.32032
  7. [7] J. Michel - A. Perotti, Ck-Regularity for the ∂-equation on Strictly Pseudoconvex Domains with Piecewise Smooth Boundaries. Math. Z.203 (1990), 415-427. Zbl0673.32019
  8. [8] C. Miranda, Istituzioni di Analisi Funzionale Lineare, vol. I. Unione Mat. Ital., Ed. Oderisi, Gubbio, 1978. 
  9. [9] M. Nacinovich, On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries. Math. Ann.281 (1988), 459-482. Zbl0628.32021MR954153
  10. [10] A. Perotti, The equation ∂u = f on the intersection of pseudoconvex domains. Rend. Mat. Acc. Lincei80 (1986), 495-500. Zbl0666.32017
  11. [11] R.M. Range - Y.T. Siu, Uniform Estimates for the ∂-Equation on Domains with Piecewise Smooth Strictly Pseudoconvex Boundaries. Math. Ann.206 (1973), 325-354. Zbl0248.32015
  12. [12] R.T. Seeley, Extension of C∞-functions defined in a half space. Proc. Amer. Math. Soc.15 (1964), 625-626. Zbl0127.28403
  13. [13] G. Sorani - V. Villani, q-complete spaces and cohomology. Trans. Amer. Math. Soc.125 (1966), 432-448. Zbl0155.40203MR206335
  14. [14] K. Peters, Solution operators for the ∂-equation on non-transversal intersections of strictly pseudoconvex domains. Math. Ann.291 (1991), 617-641. Zbl0748.32010

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