TY - JOUR
T1 - Integral formulas of the Hilbert, Poincaré-Bertrand, Schwarz and Poisson type for the β–analytic function theory
AU - Bory-Reyes, Juan
AU - Abreu-Blaya, Ricardo
AU - Pérez-de la Rosa, Marco Antonio
AU - Schneider, Baruch
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
PY - 2020/12/15
Y1 - 2020/12/15
N2 - In the present work we obtain some analogues of the Hilbert formulas on the unit circle and on the upper half-plane for the theory of solutions of a special case of the Beltrami equation in C to be referred as β-analytic functions. Furthermore, a Poincaré–Bertrand formula related to the β-Cauchy singular integral over a closed Jordan curve is derived and it is used to derive the corresponding Schwarz and Poisson formulas.
AB - In the present work we obtain some analogues of the Hilbert formulas on the unit circle and on the upper half-plane for the theory of solutions of a special case of the Beltrami equation in C to be referred as β-analytic functions. Furthermore, a Poincaré–Bertrand formula related to the β-Cauchy singular integral over a closed Jordan curve is derived and it is used to derive the corresponding Schwarz and Poisson formulas.
KW - Hilbert formulas
KW - Poincaré–Bertrand formulas
KW - Poisson formulas
KW - Schwarz formulas
KW - β–analytic functions
UR - http://www.scopus.com/inward/record.url?scp=85089573600&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2020.124493
DO - 10.1016/j.jmaa.2020.124493
M3 - Artículo
AN - SCOPUS:85089573600
SN - 0022-247X
VL - 492
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
M1 - 124493
ER -