Ágota G. Horváth: Fractional Bessel operators, Bessel-Sobolev and Bessel B-potential spaces

Examination of fractional Bessel operators of elliptic type leads to the study of the corresponding function spaces. The generalized or Bessel translation implies the notion of different Bessel moduli of smoothness. The equivalence of modulus of smoothness and the appropriate K-functional allows to define a Gagliardo-type seminorm and fractional Bessel-Sobolev spaces as well. We also define the Bessel B-potential spaces, and give embedding theorems. As an application, a potential theoretic characterization of removable sets with respect to certain fractional partial differential operators is given.
(Joint work with Mouna Chegaar.)