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In this paper, we investigate a family of holomorphic functions in several complex variables concerning the total derivative (or called radial derivative), and obtain some well-known normality criteria such as the Miranda's theorem, the Marty's theorem and results on the Hayman's conjectures in several complex variables. A high-dimension version of the famous Zalcman's lemma for normal families is also given.
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참고문헌 (37)
참고문헌 신청
D. Bargmann / 1999 / Families of meromorphic functions avoiding continuous functions / J. Anal. Math 79:379~387
W. Bergweiler / 1995 / On the singularities of the inverse to a mermorphic function of finite order / Rev. Mat. Iberoam 11(2):335~373
A. Bloch / 1926 / Sur les syst`emes de fonctions holomorphes `a vari´et´es lin´eaires lacunaires / Ann. Sci. Ecole Norm. Sup 43(3):309~362
H. H. Chen / 1995 / On value distribution of f nf ′ / Sci. China Ser. A 38:789~798
Q. Chen / 2013 / A general differential inequality of the k-th derivative that leads to normality / Ann. Acad. Sci. Fenn. Math 38(2):691~695
W. Bergweiler / 1995 / On the singularities of the inverse to a mermorphic function of finite order / Rev. Mat. Iberoam 11(2):335~373
A. Bloch / 1926 / Sur les syst`emes de fonctions holomorphes `a vari´et´es lin´eaires lacunaires / Ann. Sci. Ecole Norm. Sup 43(3):309~362
H. H. Chen / 1995 / On value distribution of f nf ′ / Sci. China Ser. A 38:789~798
Q. Chen / 2013 / A general differential inequality of the k-th derivative that leads to normality / Ann. Acad. Sci. Fenn. Math 38(2):691~695
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