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

DOI

10.3906/mat-1704-77

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

First Page

862

Last Page

875

Recommended Citation

REYES, JUAN BORY; BLAYA, RICARDO ABREU; ROSA, MARCO ANTONIO PEREZ DE LA; and SCHNEIDER, BARUCH (2018) "On the Hilbert formulas and of change of integration order for some singular integrals in the unit circle," Turkish Journal of Mathematics: Vol. 42: No. 3, Article 10. https://doi.org/10.3906/mat-1704-77
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/10