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Licensed Unlicensed Requires Authentication Published by De Gruyter June 14, 2016

The Riesz potential in generalized Orlicz spaces

Petteri Harjulehto and Peter Hästö EMAIL logo
From the journal Forum Mathematicum

Abstract

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

MSC 2010: 46E30; 42B20

Communicated by Frank Duzaar


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Received: 2015-11-25
Published Online: 2016-6-14
Published in Print: 2017-1-1

© 2017 by De Gruyter

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