Kobayashi-Royden vs. Hahn pseudometric in ℂ²

Witold Jarnicki

Displaying similar documents to “Kobayashi-Royden vs. Hahn pseudometric in ℂ²”

A limit involving functions in $W_{0}^{1, p} (Ω)$

Biagio Ricceri (1999)

Colloquium Mathematicae

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We point out the following fact: if Ω ⊂ $ℝ^{n}$ is a bounded open set, δ>0, and p>1, then $l i m_{\to 0^{+}} i n f_{\in V} \int_{Ω} {| \nabla (x) |}^{p} d x = \infty$ , where $V_{=} \in W_{0}^{1, p} (Ω) : m e a s (x \in Ω : | (x) | > δ) > .$

Certain partial differential subordinations on some Reinhardt domains in $ℂ^{n}$

Gabriela Kohr, Mirela Kohr (1997)

Annales Polonici Mathematici

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We obtain an extension of Jack-Miller-Mocanu’s Lemma for holomorphic mappings defined in some Reinhardt domains in $ℂ^{n}$ . Using this result we consider first and second order partial differential subordinations for holomorphic mappings defined on the Reinhardt domain $B_{2 p}$ with p ≥ 1.

Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in $C^{n}$ with real analytic boundary

Andrea Iannuzzi (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is shown that given a bounded strictly convex domain $Ω$ in $C^{n}$ with real analitic boundary and a point $x_{0}$ in $Ω$ , there exists a larger bounded strictly convex domain $Ω^{'}$ with real analitic boundary, close as wished to $Ω$ , such that $Ω$ is a ball for the Kobayashi distance of $Ω^{'}$ with center $x_{0}$ . The result is applied to prove that if $Ω$ is not biholomorphic to the ball then any automorphism of $Ω$ extends to an automorphism of $Ω^{'}$ .

Canonical mappings in $Σ_{M} (D)$

Z. Abdul-Hadi, D. Bschouty, W. Hengartner (1985)

Matematički Vesnik

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Rigidity of the holomorphic automorphism of the generalized Fock-Bargmann-Hartogs domains

Ting Guo, Zhiming Feng, Enchao Bi (2021)

Czechoslovak Mathematical Journal

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We study a class of typical Hartogs domains which is called a generalized Fock-Bargmann-Hartogs domain $D_{n, m}^{p} (μ)$ . The generalized Fock-Bargmann-Hartogs domain is defined by inequality $e^{{μ ∥ z ∥}^{2}} \sum_{j = 1}^{m} {| ω_{j} |}^{2 p} < 1$ , where $(z, ω) \in ℂ^{n} \times ℂ^{m}$ . In this paper, we will establish a rigidity of its holomorphic automorphism group. Our results imply that a holomorphic self-mapping of the generalized Fock-Bargmann-Hartogs domain $D_{n, m}^{p} (μ)$ becomes a holomorphic automorphism if and only if it keeps the function $\sum_{j = 1}^{m} {| ω_{j} |}^{2 p} e^{{μ ∥ z ∥}^{2}}$ invariant.

The exceptional sets for functions of the Bergman space in the unit ball

Piotr Jakóbczak (1993)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $D$ be a domain in $C^{2}$ . Given $w \in C$ , set $D_{w} = \{z \in C ∣ (z, w) \in D\}$ . If $f$ is a holomorphic and square-integrable function in $D$ , then the set $E (D, f)$ of all $w$ such that $f (\cdot, w)$ is not square-integrable in $D_{w}$ has measure zero. We call this set the exceptional set for $f$ . In this Note we prove that whenever $0 < r < 1$ there exists a holomorphic square-integrable function $f$ in the unit ball $B$ in $C^{2}$ such that $E (B, f)$ is the circle $C (0, r) = \{z \in C ∣ |z| = r\}$ .

Global analytic and Gevrey surjectivity of the Mizohata operator $D_{2} + i x_{2}^{2 k} D_{1}$

Lamberto Cattabriga, Luisa Zanghirati (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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The surjectivity of the operator $D_{2} + i x_{2}^{2 k} D_{1}$ from the Gevrey space $E^{\{s\}} (R^{2})$ , $s \geq 1$ , onto itself and its non-surjectivity from $E^{\{s\}} (R^{3})$ to $E^{\{s\}} (R^{3})$ is proved.

Balanced domains of holomorphy of type $H^{α}$

J. Siciak (1985)

Matematički Vesnik

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On n-circled $ℋ^{\infty}$ -domains of holomorphy

Marek Jarnicki, Peter Pflug (1997)

Annales Polonici Mathematici

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We present various characterizations of n-circled domains of holomorphy $G \subset ℂ^{n}$ with respect to some subspaces of $ℋ^{\infty} (G)$ .