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 $\alpha$-hy\-per\-ho\-lo\-mor\-phic 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 Poincaré-Bertrand formula for the $\alpha$-hyperholomorphic singular integrals in the unit circle is presented.