Transactions of the American Mathematical Society

Author(s): Filippo Bracci
Journal: Trans. Amer. Math. Soc. 355 (2003), 2569-2584.
MSC (2000): Primary 30D05; Secondary 30C80, 30E25, 47B33
Posted: January 29, 2003
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Abstract: Let $\Delta$ be the unit disc of $\mathbb C$ and let $f,g \in \mathrm{Hol}(\Delta,\Delta)$ be such that $f \circ g = g \circ f$ . For

, let $\mathrm{Fix}_A (f):=\{p \in \partial\Delta \mid \lim_{r \to 1}f(rp)=p, \lim_{r \to 1}\vert f'(rp)\vert\leq A \}$ . We study the behavior of

on $\mathrm{Fix}_A (f)$ . In particular, we prove that $g(\mathrm{Fix}_A (f))\subseteq \mathrm{Fix}_A (f)$ . As a consequence, besides conditions for $\mathrm{Fix}_A(f) \cap \mathrm{Fix}_A(g) \neq \emptyset$ , we prove a conjecture of C. Cowen in case

and

are univalent mappings.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30D05, 30C80, 30E25, 47B33

Filippo Bracci
Affiliation: Dipartimento di Matematica, Università di Roma ``Tor Vergata'', Via della Ricerca Scientifica 1, 00133 Roma, Italy
Email: fbracci@mat.uniroma2.it

DOI: 10.1090/S0002-9947-03-03170-2
PII: S 0002-9947(03)03170-2
Keywords: Fixed points; Wolff point; commuting mappings
Received by editor(s): April 1, 2001
Posted: January 29, 2003
Additional Notes: Partially supported by Progetto MURST di Rilevante Interesse Nazionale {\it Proprietà geometriche delle varietà reali e complesse} and GNSAGA
Copyright of article: Copyright 2003, American Mathematical Society

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