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The Riesz potential in generalized Orlicz spaces

  • Petteri Harjulehto und Peter Hästö EMAIL logo
Veröffentlicht/Copyright: 14. Juni 2016

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

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