On the Green function for the weighted biharmonic operator \(\Delta w^{-1}\Delta\) in the unite disk
type: Item
instance of: scholarly article
zbMATH Open document ID: 1074.31501
publication date: 2001-06-10T00:00:00Z
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 35J30
Mathematics Subject Classification ID: 35A25
zbMATH DE Number: 1603275
zbMATH Keywords: weighted biharmonic operator
zbMATH Keywords: Green function
zbMATH Keywords: Bergmann space
author: S. M. Shimorin
MaRDI profile type: Publication
title: On the Green function for the weighted biharmonic operator \(\Delta w^{-1}\Delta\) in the unite disk
published in: Problemy Matematicheskogo Analiza
review text: The aim of the article is to prove positivity of the Green function for the weighted biharmonic operator \(\Delta w^{-1}\Delta\) in the unit disk \(\mathbb D\) in the case when the weighted function \(w\) is an arbitrary radial and logarithmic subharmonic positive function (summable) on \(\mathbb D\). The result obtained makes it possible to bring into consideration the Bergmann class of functions that possesses the so-called factorization property. This property is the well-known analog of the internally-exterior factorization for the Hardy classes.
reviewed by: Vladimir N. Grebenev
description: scientific article; zbMATH DE number 1603275