On balanced L²-domains of holomorphy

Marek Jarnicki; Peter Pflug

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

Invariant pseudodistances and pseudometrics - completeness and product property

Marek Jarnicki, Peter Pflug (1991)

Annales Polonici Mathematici

Similarity:

A survey of properties of invariant pseudodistances and pseudometrics is given with special stress put on completeness and product property.

On Lempert functions in $ℂ^{2}$ .

Jarnicki, Witold (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Similarity:

New examples of effective formulas for holomorphically contractible functions

Marek Jarnicki, Peter Pflug (1999)

Studia Mathematica

Similarity:

Let $G \subset ℂ^{n}$ and $B \subset ℂ^{m}$ 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.

A polyharmonic analogue of a Lelong theorem and polyhedric harmonicity cells.

Boutaleb, Mohamed (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Similarity:

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

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

Annales Polonici Mathematici

Similarity:

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 $f \in H^{p} (α)$ : (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) $Ω = w = (w ₁, . . ., w_{n}) \in ℂ^{n} : I m w ₁ > \sum_{k = 2}^{n} | w_{k} | ²$ , $K (w) = I m w ₁ - \sum_{k = 2}^{n} | w_{k} | ²$ ; 2) Ω is the matrix domain consisting of those...

The Helmholtz decomposition in arbitrary unbounded domains - a theory beyond

Farwig, Reinhard, Kozono, Hideo, Sohr, Hermann

Similarity:

Holomorphic functions with singularities on algebraic sets.

Sičiak, Józef (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Similarity:

Envelopes of holomorphy for solutions of the Laplace and Dirac equations

Martin Kolář (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Analytic continuation and domains of holomorphy for solution to the complex Laplace and Dirac equations in $𝐂^{n}$ are studied. First, geometric description of envelopes of holomorphy over domains in $𝐄^{n}$ is given. In more general case, solutions can be continued by integral formulas using values on a real $n - 1$ dimensional cycle in $𝐂^{n}$ . Sufficient conditions for this being possible are formulated.