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Distortion Properties of Holomorphic Functions of Several Complex Variables

✍ Scribed by Ryszard Mazur

Publisher
John Wiley and Sons
Year
1980
Tongue
English
Weight
219 KB
Volume
99
Category
Article
ISSN
0025-584X

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✦ Synopsis

Distort.ion Properties of Holomorphic

Functions of Several Complex Variables By RYSZARD l &bZUR of Kielce (Poland) (Eingegtlngen am 9.7.1980) Abstract.. Let Q(D) be a class of funct,ions q, q(0) = 0, Iq(z)l < 1 holomorphic in the REINHAUDT domain D c Cn, a and barbitrary fixed numbers satisfying the condition -1 5 b < a s 1. p(a, b ; U )the class of functions p such that p E @(a, b ; D ) iff for soiiie q E Q(D) and every z E D. S*(n. b ; D)the class of functions f such that f E &'*(a, g; D ) iff Sc((a, b ; D ) -the class of functions q such that q E Sc(a, b ; D) iff where p E @(a, b ; D ) and K is an operator of the form K(h(z)) = zkh:,(z) for z = ( z l , z2, ..., zn). k -1 The author obtains sharp bounds on lp(z)l, If(z)l and Ig(z)l jiiequalities for functions in p(a, b ; D ) , S*(a, b ; D) and Sc(a, b ; U ) . well as sharp coefficient

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In the first part, we generalize the classical result of Bohr by proving that an m Ε½ analogous phenomenon occurs whenever D is an open domain in ‫ރ‬ or, more . Ε½ . Ο± generally, a complex manifold and is a basis in the space of holomorphic n ns0 Ε½ . Ε½ . functions H D such that s 1 and z s 0, n G 1,