On the Hilbert formulas and of change of integration order for some singular integrals in the unit circle

Abstract

We obtain some analogues of the Hilbert formulas on the unit circle for alpha-hyperholomorphic function theory when alpha is a complex number. Such formulas relate a pair of components of the boundary value of an alpha-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincare-Bertrand formula for the alpha-hyperholomorphic singular integrals in the unit circle is presented.