Kato space for Dirichlet forms
type: Item
instance of: scholarly article
title: Kato space for Dirichlet forms
zbMATH Open document ID: 0943.31004
DOI: 10.1023/A:1008684104029
author: Marco Biroli
author: Umberto Mosco
published in: Potential Analysis
publication date: 1999-09-07T00:00:00Z
review text: The authors consider a wide class of regular Dirichlet forms of diffusion type incuding elliptic and subelliptic operators. For these Dirichlet forms the notion of Kato space is introduced and it is proved that the Kato space becomes a Banach space when suitably normed. The main theorem states that a positive Radon measure \(\mu\) belongs to the dual of the form domain if and only if \[ \int G(x,y) d\mu(x) d\mu(y)< \infty, \] where \(G\) is the Green function. It is then proved that a weak solution of the equation \(Lu=f\), \(L\) being the generator of the form, is continuous if \(\mu\) belongs to the Kato space.
reviewed by: André Noll
Mathematics Subject Classification ID: 31C25
Mathematics Subject Classification ID: 35D10
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 1333168
zbMATH Keywords: regular Dirichlet forms of diffusion type
zbMATH Keywords: elliptic and subelliptic operators
zbMATH Keywords: Kato space
zbMATH Keywords: Radon measure
zbMATH Keywords: Green function
MaRDI profile type: Publication
full work available at URL: a:1008684104029
OpenAlex ID: W9060799
description: scientific article; zbMATH DE number 1333168