University of Oulu

Forum Mathematicum, Volume 29, Issue 1, Pages 229–244, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI:

The Riesz potential in generalized Orlicz spaces

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Author: Harjulehto, Petteri1; Hästö, Peter2
Organizations: 1Department of Mathematics and Statistics, FI-20014 University of Turku, Finland
2Department of Mathematical Sciences, FI-90014 University of Oulu, Finland
Format: article
Version: accepted version
Access: open
Online Access: PDF Full Text (PDF, 0.2 MB)
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Language: English
Published: De Gruyter, 2017
Publish Date: 2019-03-28


In this article we prove a Riesz potential estimate and a Sobolev inequality for general generalized Orlicz spaces. Our assumptions are natural generalizations of the log-Hölder continuity that is commonly used in the variable exponent case. We also provide a number of useful auxiliary results including a normalization of the Φ-function and its behavior under duality.

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Series: Forum mathematicum
ISSN: 0933-7741
ISSN-E: 1435-5337
ISSN-L: 0933-7741
Volume: 29
Issue: 1
Pages: 229 - 244
DOI: 10.1515/forum-2015-0239
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Copyright information: © 2017 by De Gruyter.