Generalized Sobolev-Orlicz spaces based on the Riesz fractional gradient as interpolation and potential spaces

Abstract

In this work we establish that the recently introduced fractional Sobolev spaces based on the Riesz fractional gradient of Musielak-Orlicz functions by one of the authors, coincide with the space of Bessel potentials of functions on such generalized Orlicz setting. Moreover, we identify them as complex interpolation spaces, and exploiting the well known properties for interpolation of operators we obtain several structural properties for those spaces.