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

Pages : 862-875

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Publication Date : 0000-00-00

Article Type : Research Paper

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