Regularity of the tangential Cauchy-Riemann complex and applications

Joachim Michel

Banach Center Publications (1995)

  • Volume: 31, Issue: 1, page 263-273
  • ISSN: 0137-6934

How to cite

top

Michel, Joachim. "Regularity of the tangential Cauchy-Riemann complex and applications." Banach Center Publications 31.1 (1995): 263-273. <http://eudml.org/doc/262699>.

@article{Michel1995,
author = {Michel, Joachim},
journal = {Banach Center Publications},
keywords = {tangential Cauchy-Riemann complex; regularity},
language = {eng},
number = {1},
pages = {263-273},
title = {Regularity of the tangential Cauchy-Riemann complex and applications},
url = {http://eudml.org/doc/262699},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Michel, Joachim
TI - Regularity of the tangential Cauchy-Riemann complex and applications
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 263
EP - 273
LA - eng
KW - tangential Cauchy-Riemann complex; regularity
UR - http://eudml.org/doc/262699
ER -

References

top
  1. [1] T. Akahori, A new approach to the local embedding theorem of CR structures for n ≥ 4, Mem. Amer. Math. Soc. 366 (1987). Zbl0628.32025
  2. [2] A. Andreotti and C. D. Hill, Convexity and the Hans Lewy Problem I, II, Ann. Scuola Norm. Sup. Pisa 26 (1971), 325-363, 747-806. 
  3. [3] A. Boggess, Kernels for the tangential Cauchy-Riemann equations, Trans. Amer. Math. Soc. 262 (1980), 1-49. Zbl0489.32014
  4. [4] A. Boggess and M. C. Shaw, A kernel approach to the local solvability of the tangential Cauchy-Riemann equations, ibid. 289 (1985), 643-658. Zbl0579.35062
  5. [5] J. Bruna and J. M. Burgués, Holomorphic approximation and estimates for the ∂̅-equation on strictly pseudoconvex non-smooth domains, Duke Math. J. 55 (1987), 539-596. Zbl0645.32009
  6. [6] G. M. Henkin, The Lewy equation and analysis on pseudoconvex manifolds, Russian Math. Surveys. 32 (1977), 59-130. Zbl0382.35038
  7. [7] J. J. Kohn and H. Rossi, On the extension of holomorphic functions from the boundary of a complex manifold, Ann. of Math. 81 (1965), 451-472. Zbl0166.33802
  8. [8] M. Kuranishi, Strongly pseudoconvex CR structures over small balls, ibid., I, 115 (1982), 451-500; II, 116 (1982), 1-64; III, 116 (1982), 249-330. Zbl0505.32018
  9. [9] H. Lewy, On the local character of the solution of an atypical linear differential equation in three variables and a related theorem for regular functions of two complex variables, ibid. 64 (1956), 514-522. Zbl0074.06204
  10. [10] I. Lieb and R. M. Range, Lösungsoperatoren für den Cauchy-Riemann Komplex mit C k -Abschätzungen, Math. Ann. 253 (1980), 145-164. Zbl0441.32007
  11. [11] L. Ma, Hölder and L p -estimates for the ∂̅-equation on non-smooth strictly q-convex domains, Manuscripta Math. 74 (1992), 177-193. Zbl0754.35092
  12. [12] L. Ma and J. Michel, Local regularity for the tangential Cauchy-Riemann complex, J. Reine Angew. Math. 442 (1993), 63-90. Zbl0781.32022
  13. [13] L. Ma and J. Michel, Regularity of local embeddings of strictly pseudoconvex CR structures, ibid. 447 (1994), 147-164. Zbl0791.32007
  14. [14] L. Ma and J. Michel, On the regularity of CR structures for almost CR vector bundles, Math. Z. 218 (1995), 135-142. Zbl0816.32016
  15. [15] B. Malgrange, Ideals of Differentiable Functions, Oxford University Press, Oxford, 1966. 
  16. [16] J. Michel, Randregularität des ∂̅-Problems für die Halbkugel im n , Manuscripta Math. 55 (1986), 239-268. Zbl0592.32016
  17. [17] J. Michel, Randregularität des ∂̅-Problems für stückweise streng pseudokonvexe Gebiete in n , Math. Ann. 280 (1988), 46-68. 
  18. [18] K. Peters, Lösungsoperatoren für die ∂̅-Gleichung auf nichttransversalen Durchschnitten streng pseudokonvexer Gebiete, Diss. A, Berlin, 1990. 
  19. [19] R. M. Range and Y. T. Siu, Uniform estimates for the ∂̅-equation on domains with piecewise smooth strictly pseudoconvex boundaries, Math. Ann. 206 (1973), 325-354. Zbl0248.32015
  20. [20] A. V. Romanov, A formula and estimates for solutions of the tangential Cauchy-Riemann equation, Mat. Sb. 99 (1976), 58-83 (in Russian). 
  21. [21] R. T. Seeley, Extensions of C -functions defined in a half space, Proc. Amer. Math. Soc. 15 (1964), 625-626. Zbl0127.28403
  22. [22] M. C. Shaw, Hölder and L p -estimates for ̅ b on weakly pseudoconvex boundaries in 2 , Math. Ann. 279 (1988), 635-652. Zbl0617.32031
  23. [23] M. C. Shaw, L p -estimates for local solutions of ̅ b on strongly pseudoconvex CR manifolds, ibid. 288 (1990), 35-62. 
  24. [24] M. C. Shaw, Optimal Hölder and L p -estimates for ̅ b on the boundaries of real ellipsoids in n , Trans. Amer. Math. Soc. 324 (1991), 213-234. 
  25. [25] S. Webster, On the local solution of the tangential Cauchy-Riemann equations, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), 167-182. Zbl0679.32019
  26. [26] S. Webster, On the proof of Kuranishi's embedding theorem, ibid., 183-207. Zbl0679.32020
  27. [27] S. Webster, A new proof of the Newlander-Nirenberg theorem, Math. Z. 201 (1989), 303-316. Zbl0651.32004
  28. [28] S. Webster, The integrability problem for CR vector bundles, in: Proc. Sympos. Pure Math. 52 (1991), 355-368. Zbl0744.32002

NotesEmbed ?

top

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.