TY - JOUR
T1 - A Martinelli-Bochner formula on fractal domains
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
N1 - Funding Information:
the paper was written, for the invitation and hospitality. The CAPES-MES project 028/07 and CNPq supported them.
PY - 2009/4
Y1 - 2009/4
N2 - A new perspective on a Cauchy integral formula for Clifford algebras valued functions on domains with quite smooth boundaries was discussed in [5]. On the other hand, the Cauchy transform associated to Clifford analysis has been involved recently with fractional metric dimensions and fractals, see [1, 2, 3]. In this paper we consider the question of possible generalizations of the Cauchy integral formula to domains with fractal boundary. As an application, we prove a Martinelli-Bochner type formula for several complex variables on such pathological domains. The proof makes heavy use of the isotonic approach of the monogenic functions theory.
AB - A new perspective on a Cauchy integral formula for Clifford algebras valued functions on domains with quite smooth boundaries was discussed in [5]. On the other hand, the Cauchy transform associated to Clifford analysis has been involved recently with fractional metric dimensions and fractals, see [1, 2, 3]. In this paper we consider the question of possible generalizations of the Cauchy integral formula to domains with fractal boundary. As an application, we prove a Martinelli-Bochner type formula for several complex variables on such pathological domains. The proof makes heavy use of the isotonic approach of the monogenic functions theory.
KW - Clifford analysis
KW - Fractals
KW - Martinelli-Bochner formula
UR - http://www.scopus.com/inward/record.url?scp=67349119200&partnerID=8YFLogxK
U2 - 10.1007/s00013-009-3049-x
DO - 10.1007/s00013-009-3049-x
M3 - Artículo
SN - 0003-889X
VL - 92
SP - 335
EP - 343
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 4
ER -