Displaying similar documents to “On balanced L²-domains of holomorphy”

On Lempert functions in ℂ 2 .

Jarnicki, Witold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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New examples of effective formulas for holomorphically contractible functions

Marek Jarnicki, Peter Pflug (1999)

Studia Mathematica

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Let G ⊂ ℂ n and B ⊂ ℂ m be domains and let Φ:G → B be a surjective holomorphic mapping. We characterize some cases in which invariant functions and pseudometrics on G can be effectively expressed in terms of the corresponding functions and pseudometrics on B.

Integral representations for some weighted classes of functions holomorphic in matrix domains

M. M. Djrbashian, A. H. Karapetyan (1991)

Annales Polonici Mathematici

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In 1945 the first author introduced the classes H p ( α ) , 1 ≤ p<∞, α > -1, of holomorphic functions in the unit disk with finite integral (1) ∬ |f(ζ)|p (1-|ζ|²)α dξ dη < ∞ (ζ=ξ+iη) and established the following integral formula for f ∈ H p ( α ) : (2) f(z) = (α+1)/π ∬ f(ζ) ((1-|ζ|²)α)/((1-zζ̅)2+α) dξdη, z∈ . We have established that the analogues of the integral representation (2) hold for holomorphic functions in Ω from the classes L p ( Ω ; [ K ( w ) ] α d m ( w ) ) , where: 1) Ω = w = ( w ₁ , . . . , w n ) ∈ ℂ n : I m w ₁ > ∑ k = 2 n | w k | ² , K ( w ) = I m w ₁ - ∑ k = 2 n | w k | ² ; 2) Ω is the matrix domain consisting of those...