The Riesz potential in generalized Orlicz spaces



: Harjulehto P, Hasto P

Publisher: WALTER DE GRUYTER GMBH

: 2017

: Forum Mathematicum

: FORUM MATHEMATICUM

: FORUM MATH

: 29

: 1

: 229

: 244

: 16

: 0933-7741

: 1435-5337

DOI: https://doi.org/10.1515/forum-2015-0239


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-Holder continuity that is commonly used in the variable exponent case. We also provide a number of useful auxiliary results including a normalization of the Phi-function and its behavior under duality



Last updated on 2024-26-11 at 12:16