Computational Methods and Function Theory 4 (2004), No. 1, 21--34
Copyright Heldermann Verlag 2004
Jerry R. Muir, Jr.
jerry.muir@rose-hulman.edu , Department of Mathematics, Rose Hulman Institute of Technology, Terre Haute, IN 47803, U.S.A.
Ted J. Suffridge
ted@ms.uky.edu , Department of Mathematics, University of Kentucky, Lexington, KY 40506, U.S.A.
For $2\leq p<\infty$, we consider convex biholomorphic mappings $F$ of the $p$-ball $B_p = \{(z,w)\in\mathbb{C}^2:\, |z|^p+|w|^p<1\}$. In particular, we find conditions under which functions of the form $F(z,w)=(z+aw^k,w)$, where $a\in\mathbb{C}$ and $k\in\mathbb{N}$, and $F(z,w)=(f(z),g(w))$, where $f$ and $g$ are mappings of the unit disk, map $B_p$ onto convex domains in $\mathbb{C}^2$.
Keywords: Biholomorphic mapping, convex mapping, p-norm.
MSC 2000: Primary 32H02; Secondary 30C45.
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