Fractional order Sobolev spaces on Wiener space
type: Item
instance of: scholarly article
title: Fractional order Sobolev spaces on Wiener space
zbMATH Open document ID: 0792.60049
DOI: 10.1007/BF01192269
author: Shinzo Watanabe
publication date: 1994-07-14T00:00:00Z
review text: Fractional order Sobolev spaces are introduced on an abstract Wiener space and Donsker's delta functions are defined as generalized Wiener functionals belonging to Sobolev spaces with negative differentiability indices. By using these notions, the regularity in the sense of Hölder continuity of a class of conditional expectations is obtained.
Mathematics Subject Classification ID: 60H07
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 569053
zbMATH Keywords: fractional order Sobolev spaces
zbMATH Keywords: abstract Wiener space
zbMATH Keywords: Donsker's delta functions
zbMATH Keywords: generalized Wiener functionals
zbMATH Keywords: Hölder continuity
reviewed by: Shuji Watanabe
MaRDI profile type: Publication
cites work: Real Interpolation of Sobolev Spaces on Subdomains of Rn
cites work: Q3803914
cites work: Dirichlet forms and analysis on Wiener space
cites work: Q3959169
cites work: Sur les espaces d'interpolation; dualité.
cites work: Derivatives of Wiener functionals and absolute continuity of induced measures
cites work: Q5607484
cites work: Q5640160
cites work: Sobolev spaces of Wiener functionals and Malliavin's calculus
cites work: On a characterization of the Sobolev spaces over an abstract Wiener space
cites work: Positive generalized Wiener functions and potential theory over abstract Wiener spaces
cites work: Q3973617
cites work: Q4834163
full work available at URL: https://doi.org/10.1007/bf01192269
OpenAlex ID: W2083485455
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569053