# Carathéodory balls and norm balls in ${H}_{p,n}=z\in {\u2102}^{n}:\parallel z{\parallel}_{p}<1$

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 75-83
- ISSN: 0137-6934

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topSchwarz, Binyamin, and Srebro, Uri. "Carathéodory balls and norm balls in $H_{p,n} = {z ∈ ℂ^{n} :∥z∥ _{p} < 1}$." Banach Center Publications 37.1 (1996): 75-83. <http://eudml.org/doc/208619>.

@article{Schwarz1996,

abstract = {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.},

author = {Schwarz, Binyamin, Srebro, Uri},

journal = {Banach Center Publications},

keywords = {Carathéodory balls; norm balls},

language = {eng},

number = {1},

pages = {75-83},

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

url = {http://eudml.org/doc/208619},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Schwarz, Binyamin

AU - Srebro, Uri

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

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 75

EP - 83

AB - 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.

LA - eng

KW - Carathéodory balls; norm balls

UR - http://eudml.org/doc/208619

ER -

## References

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- [JP] M. Jarnicki and P. Pflug, Invariant distances and metrics in complex analysis, Walter de Gruyter, 1993. Zbl0789.32001
- [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. Zbl0812.32010
- [R] W. Rudin, Function theory in the unit ball of ${\u2102}^{n}$, Springer, New York, 1980. Zbl0495.32001
- [Sch] B. Schwarz, Carathéodory balls and norm balls of the domain $H=({z}_{1},{z}_{2})\in {\u2102}^{2}:|{z}_{1}|+|{z}_{2}|<1$, Israel J. of Math. 84 (1993), 119-128.
- [Sr] U. Srebro, Carathéodory balls and norm balls in $H=z\in {\u2102}^{n}:\parallel z{\parallel}_{1}<1$, Israel J. Math. 89 (1995), 61-70.
- [Z] W. Zwonek, Carathéodory balls and norm balls of the domains ${H}_{n}=z\in {\u2102}^{n}:|{z}_{1}|+...+|{z}_{n}|<1$, Israel J. Math. 89 (1995), 71-76. Zbl0824.32007