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

Authors: JUAN BORY REYES, RICARDO ABREU BLAYA, MARCO ANTONIO PEREZ DE LA ROSA, BARUCH SCHNEIDER

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.

Keywords: Hilbert formulas, Poincaré-Bertrand formulas

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