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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 ⊂ n is a bounded open set, δ>0, and p>1, then l i m 0 + i n f V Ω | ( x ) | p d x = , where V = W 0 1 , p ( Ω ) : m e a s ( x Ω : | ( x ) | > δ ) > .

Certain partial differential subordinations on some Reinhardt domains in 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 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 .

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 j = 1 m | ω j | 2 p < 1 , where ( z , ω ) n × 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 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 C , set D w = z C z , w D . If f is a holomorphic and square-integrable function in D , then the set E D , f of all w such that f ( , 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 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 1 , onto itself and its non-surjectivity from E s R 3 to E s R 3 is proved.

On n-circled -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 n with respect to some subspaces of ( G ) .