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The Bergman kernel functions of certain unbounded domains

100%

Haslinger F.

Annales Polonici Mathematici

1998

tom 70

nr 1

109-115

We compute the Bergman kernel functions of the unbounded domains $Ω_p = {(z',z) ∈ ℂ² : 𝕴z > p(z')}$, where $p(z') = |z'|^{α}/α$. It is also shown that these kernel functions have no zeros in $Ω_p$. We use a method from harmonic analysis to reduce the computation of the 2-dimensional case to the problem of finding the kernel function of a weighted space of entire functions in one complex variable.

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Holomorphic Sobolev spaces on the ball

52%

Beatrous F., Burbea J.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction ..............................................................5 0. Preliminaries and notation....................................6 1. Hilbert spaces of holomorphic functions..............11 2. Some estimates ..................................................16 3. The space $L^p_q$............................................22 4. Norm estimates...................................................30 5. Sobolev norms....................................................35 6. Projections in Sobolev spaces............................47 References.............................................................56

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Beatrous F.

1 Burbea J.

1 Haslinger F.

1 1998

1 1989

Wyniki wyszukiwania

The Bergman kernel functions of certain unbounded domains

Holomorphic Sobolev spaces on the ball