Spectral theory of multiplication operators on Hardy-Sobolev spaces

For a pointwise multiplier φ of the Hardy-Sobolev space Hβ2 on the open unit ball Bn in Cn, we study spectral properties of the multiplication operator Mφ:Hβ2→Hβ2. In particular, we compute the spectrum and essential spectrum of Mφ and develop the Fredholm theory for these operators.