TY - JOUR
T1 - Characterization of generalized Orlicz spaces
AU - Ferreira, Rita
AU - Hästö, Peter
AU - Ribeiro, Ana Margarida
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2018/10/11
Y1 - 2018/10/11
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/626470
UR - https://www.worldscientific.com/doi/abs/10.1142/S0219199718500797
UR - http://www.scopus.com/inward/record.url?scp=85057421917&partnerID=8YFLogxK
U2 - 10.1142/S0219199718500797
DO - 10.1142/S0219199718500797
M3 - Article
SN - 0219-1997
SP - 1850079
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
ER -