TY - JOUR
T1 - ∂̄ -problem for an overdetermined system with two higher dimensional variables
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
PY - 2011/12
Y1 - 2011/12
N2 - Our main purpose is to describe necessary and sufficient conditions for the solvability of the ∂̄ -problem for biregular complex Clifford algebra valued functions of two higher dimensional variables in even dimensional Euclidean spaces. Since the biregular function theory falls naturally from the so-called isotonic Clifford analysis, the main idea of the proof is based on the notion of biregular-conjugate harmonic functions to be introduced here. Besides, whenever the ∂̄ -problem is solvable, we give the general solution of it in a quite explicit form.
AB - Our main purpose is to describe necessary and sufficient conditions for the solvability of the ∂̄ -problem for biregular complex Clifford algebra valued functions of two higher dimensional variables in even dimensional Euclidean spaces. Since the biregular function theory falls naturally from the so-called isotonic Clifford analysis, the main idea of the proof is based on the notion of biregular-conjugate harmonic functions to be introduced here. Besides, whenever the ∂̄ -problem is solvable, we give the general solution of it in a quite explicit form.
KW - Clifford analysis
KW - Conjugate harmonic functions
KW - ∂̄-problem
UR - http://www.scopus.com/inward/record.url?scp=82755187288&partnerID=8YFLogxK
U2 - 10.1007/s00013-011-0325-3
DO - 10.1007/s00013-011-0325-3
M3 - Artículo
SN - 0003-889X
VL - 97
SP - 579
EP - 586
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 6
ER -