RMC - Vol. 5, Num. 2, 3 - Michael Langenbruch

Full paper in PDF:
$%M. Langenbruch, Splitting of the $@$ -complex in weighted spaces of square integrable functions, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 2, 3, 201–%$2.

Splitting of the $@$ -Complex in Weighted Spaces of Square Integrable Functions

Michael LANGENBRUCH

Mathematisches Institut
Einsteinstr., 62
D-4400 Münster
Bundesrepublik Deutschland

Received: April 1, 1991

ABSTRACT

The splitting of the $@$ -complex in weighted spaces of (locally) square integrable functions (defined on $_O_ < CN$ by means of an (increasing) weight system ${Wn |n > 1}$ is characterized by the following criterion on the existence of certain plurisubharmonic (psh.) functions: For any $t (- _O_$ there are psh. functions $Pt$ on $_O_$ and for any $n > 1$ there are $l(n)> n$ and $A(n) >0$ such that for any $n= 0$ and any $z,t (- _O_$ :

Pt(z)- Pt(t)> Wl(n)(z)- Wn(t)+ A(n).

(*)

This is applied to the generation of weighted algebras of holomorphic functions and to the existence of extension operators for holomorphic functions defined on strongly interpolating varieties. A systematic study of (*) is given in Langenbruch (1992).

1991 Mathematics Subject Classification: 32F20, 32F05, 30D15.