Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$

• Autorzy: Binyamin Schwarz , Uri Srebro
• Języki publikacji: EN

Abstrakty

EN

It is shown that for n ≥ 2 and p > 2, where p is not an even integer, the only balls in the Carathéodory distance on $H_{p,n} = {z ∈ ℂ^{n}: ∥ z∥_{p} < 1 }$ which are balls with respect to the complex $l_{p}$ norm in $ℂ^{n}$ are those centered at the origin.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 75-83

Daty

wydano

1996

Twórcy

autor

Binyamin Schwarz

• Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

autor

Uri Srebro

• Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel

Bibliografia

• [D] S. Dineen, The Schwarz lemma, Oxford Mathematical Monograph, Clarendon Press, 1989.
• [JP] M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis, Walter de Gruyter, 1993.
• [JPZ] M. Jarnicki, P. Pflug and R. Zeinstra, Geodesics for convex complex ellipsoids, Annali d. Scuola Normale Superiore di Pisa XX Fasc. 4 (1993), 535-543.
• [R] W. Rudin, Function theory in the unit ball of $ℂ^{n}$, Springer, New York, 1980.
• [Sch] B. Schwarz, Carathéodory balls and norm balls of the domain $H = {(z_1,z_2) ∈ ℂ^2: |z_1| + |z_2| < 1}$, Israel J. of Math. 84 (1993), 119-128.
• [Sr] U. Srebro, Carathéodory balls and norm balls in $H ={z ∈ ℂ^n: ∥z∥_1 < 1}$, Israel J. Math. 89 (1995), 61-70.
• [Z] W. Zwonek, Carathéodory balls and norm balls of the domains $H_n = {z ∈ ℂ^n: |z_1| + ... + |z_n| < 1}$, Israel J. Math. 89 (1995), 71-76.