Certain partial differential subordinations on some Reinhardt domains in ℂ n

Gabriela Kohr; Mirela Kohr

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 2, page 179-191
  • ISSN: 0066-2216

Abstract

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We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in ℂ n . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain B 2 p with p ≥ 1.

How to cite

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Gabriela Kohr, and Mirela Kohr. "Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$." Annales Polonici Mathematici 65.2 (1997): 179-191. <http://eudml.org/doc/269941>.

@article{GabrielaKohr1997,
abstract = {We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in $ℂ^n$. Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_\{2p\}$ with p ≥ 1.},
author = {Gabriela Kohr, Mirela Kohr},
journal = {Annales Polonici Mathematici},
keywords = {subordination; biholomorphic mapping; Reinhardt domain; holomorphic mappings; Reinhardt domains},
language = {eng},
number = {2},
pages = {179-191},
title = {Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$},
url = {http://eudml.org/doc/269941},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Gabriela Kohr
AU - Mirela Kohr
TI - Certain partial differential subordinations on some Reinhardt domains in $ℂ^n$
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 2
SP - 179
EP - 191
AB - We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in $ℂ^n$. Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_{2p}$ with p ≥ 1.
LA - eng
KW - subordination; biholomorphic mapping; Reinhardt domain; holomorphic mappings; Reinhardt domains
UR - http://eudml.org/doc/269941
ER -

References

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  1. [C] B. Chabat, Introduction à l'analyse complexe, tome II, Mir, Moscou, 1990. 
  2. [GW] S. Gong and S. K. Wang, A necessary and sufficient condition that biholomorphic mappings are starlike on a class of Reinhardt domains, Chinese Ann. Math. Ser. B 13 (1) (1992), 95-104. Zbl0793.32001
  3. [GWQ] S. Gong, S. K. Wang and Q. Yu, Biholomorphic convex mappings of ball in ℂ n , Pacific J. Math. 161 (1993), 287-306. Zbl0788.32017
  4. [K] K. Kikuchi, Starlike and convex mappings in several complex variables, Pacific J. Math. 44 (1973), 569-580. Zbl0262.32009
  5. [KO1] G. Kohr, On some partial differential subordinations for holomorphic mappings in ℂ n , Libertas Math. 115 (1996), 129-142. 
  6. [KO2] G. Kohr and M. Kohr-Ile, Partial differential subordinations for holomorphic mappings of several complex variables, Studia Univ. Babeş-Bolyai Math. 60 (4) (1995), 46-62. Zbl0862.32017
  7. [KO3] G. Kohr and P. Liczberski, General partial differential subordinations for holomorphic mappings in ℂ n , Math. Nachr., to appear. Zbl1011.32011
  8. [KO4] G. Kohr and C. Pintea, An extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined on some domains in ℂ n , to appear. Zbl0881.32012
  9. [L] P. Liczberski, Jack’s Lemma for holomorphic mappings in ℂ n , Ann. Univ. Mariae Curie-Skłodowska Sect. A 40 (1986), 131-140. 
  10. [MM1] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Math. Anal. Appl. 65 (1978), 289-305. Zbl0367.34005
  11. [MM2] S. S. Miller and P. T. Mocanu, Differential subordinations and inequalities in the complex plane, J. Differential Equations 67 (1987), 199-211. Zbl0633.34005
  12. [S1] T. J. Suffridge, The principle of subordination applied to functions of several variables, Pacific J. Math. 33 (1970), 241-248. Zbl0196.09601
  13. [S2] T. J. Suffridge, Starlikeness, convexity and other geometric properties of holomorphic maps in higher dimensions, in: Lecture Notes in Math. 599, Springer, 1976, 146-159. 

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