Refereed journal article or data article (A1)

Characterization of generalized Orlicz spaces




List of AuthorsFerreira Rita, Hästö Peter, Ribeiro Ana Margarida

PublisherWorld Scientific Publishing Co. Pte Ltd

Publication year2020

JournalCommunications in Contemporary Mathematics

Journal name in sourceCommunications in Contemporary Mathematics

Article number1850079

Volume number22

Issue number2

ISSN0219-1997

eISSN1793-6683

DOIhttp://dx.doi.org/10.1142/S0219199718500797


Abstract

The norm in classical Sobolev spaces can be expressed as a difference
quotient. This expression can be used to generalize the space to the
fractional smoothness case. Because the difference quotient is based on
shifting the function, it cannot be used in generalized Orlicz spaces.
In its place, we introduce a smoothed difference quotient and show that
it can be used to characterize the generalized Orlicz–Sobolev space. Our
results are new even in Orlicz spaces and variable exponent spaces.


Last updated on 2023-03-10 at 14:49