TY - JOUR
T1 - ∂̄-problem in domains of C 2 in terms of hyper-conjugate harmonic functions
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Luna-Elizarrarás, María Elena
AU - Shapiro, Michael
N1 - Funding Information:
The research carried out in this article was initiated when the second author was visiting the Escuela Superior de Física y Matemáticas, IPN, México City. He sincerely acknowledges invitation, hospitality and support. The Mexican authors were partially supported by CONACYT projects as well as by Instituto Politécnico Nacional in the framework of COFAA and SIP programs. The authors are grateful to the anonymous referee for helpful suggestions and comments.
PY - 2012/7
Y1 - 2012/7
N2 - Given a Jordan domain of C 2, we consider the ∂̄-problem and establish a necessary and sufficient condition for its solvability in terms of the existence of hyper-conjugate harmonic functions, a notion coming from quaternionic analysis. Besides, whenever the ∂̄-problem is solvable we give its general solution in a quite explicit form.
AB - Given a Jordan domain of C 2, we consider the ∂̄-problem and establish a necessary and sufficient condition for its solvability in terms of the existence of hyper-conjugate harmonic functions, a notion coming from quaternionic analysis. Besides, whenever the ∂̄-problem is solvable we give its general solution in a quite explicit form.
KW - Borel-Pompeiu formula
KW - Cauchy-Fueter operator
KW - Théodoresco operator
KW - hyper-conjugate harmonic functions
KW - ∂̄-problem
UR - http://www.scopus.com/inward/record.url?scp=84863908347&partnerID=8YFLogxK
U2 - 10.1080/17476933.2011.598933
DO - 10.1080/17476933.2011.598933
M3 - Artículo
SN - 1747-6933
VL - 57
SP - 743
EP - 749
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 7-8
ER -