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

Juan Bory Reyes; Ricardo Abreu Blaya; Marco Antonio Pérez De La Rosa; Baruch Schneider

doi:10.3906/mat-1704-77

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

Juan Bory Reyes, Ricardo Abreu Blaya, Marco Antonio Pérez De La Rosa, Baruch Schneider

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

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4 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	862-875
Number of pages	14
Journal	Turkish Journal of Mathematics
Volume	42
Issue number	3
DOIs	https://doi.org/10.3906/mat-1704-77
State	Published - 2018

Keywords

Hilbert formulas
Poincaré-Bertrand formulas

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10.3906/mat-1704-77

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abstract = "We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory when α is a complex number. Such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincar{\'e}-Bertrand formula for the α- hyperholomorphic singular integrals in the unit circle is presented.",

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AU - Bory Reyes, Juan

AU - Abreu Blaya, Ricardo

AU - Pérez De La Rosa, Marco Antonio

AU - Schneider, Baruch

N1 - Publisher Copyright: © TÜBI˙KTAK.

PY - 2018

Y1 - 2018

N2 - We obtain some analogues of the Hilbert formulas on the unit circle for α-hyperholomorphic function theory when α is a complex number. Such formulas relate a pair of components of the boundary value of an α-hyperholomorphic function in the unit circle with the other one. Furthermore, the corresponding Poincaré-Bertrand formula for the α- hyperholomorphic singular integrals in the unit circle is presented.

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

KW - Hilbert formulas

KW - Poincaré-Bertrand formulas

UR - http://www.scopus.com/inward/record.url?scp=85046727553&partnerID=8YFLogxK

U2 - 10.3906/mat-1704-77

DO - 10.3906/mat-1704-77

M3 - Artículo

SN - 1300-0098

VL - 42

SP - 862

EP - 875

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

IS - 3

ER -

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

Abstract

Keywords

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