Fractional Bessel–Sobolev and Bessel B-potential spaces

Abstract

After proving the equivalence of the Bessel $K$-functional and the corresponding spherical modulus of smoothness we define fractional Bessel–Sobolev spaces. As an analog of the classical one the imbedding relation of fractional Bessel–Sobolev and Bessel B-potential spaces is pointed out. Applying the defined notions a potential theoretic characterization of removable sets with respect to a certain fractional partial differential operator is derived.