TY - JOUR
T1 - Criteria for monogenicity of Clifford algebra-valued functions on fractal domains
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
N1 - Funding Information:
Acknowledgements. The authors wish to thank the IMPA, Rio de Janeiro, where the paper was written, for the invitation and hospitality. The CAPES-MES project 028/07 and CNPq supported them.
PY - 2010
Y1 - 2010
N2 - Suppose that Ω is a bounded domain with fractal boundary Γ in ℝn+1 and let ℝ0,n be the real Clifford algebra constructed over the quadratic space ℝn. Furthermore, let U be a ℝ0,n-valued function harmonic in Ω and Hölder-continuous up to Γ. By using a new Clifford Cauchy transform for Jordan domains in ℝn+1 with fractal boundaries, we give necessary and sufficient conditions for the monogenicity of U in terms of its boundary value u = U{pipe}Γ. As a consequence, the results of Abreu Blaya et al. (Proceedings of the 6th International ISAAC Congress Ankara, 167- 174, World Scientific) are extended, which require Γ to be Ahlfors-David regular.
AB - Suppose that Ω is a bounded domain with fractal boundary Γ in ℝn+1 and let ℝ0,n be the real Clifford algebra constructed over the quadratic space ℝn. Furthermore, let U be a ℝ0,n-valued function harmonic in Ω and Hölder-continuous up to Γ. By using a new Clifford Cauchy transform for Jordan domains in ℝn+1 with fractal boundaries, we give necessary and sufficient conditions for the monogenicity of U in terms of its boundary value u = U{pipe}Γ. As a consequence, the results of Abreu Blaya et al. (Proceedings of the 6th International ISAAC Congress Ankara, 167- 174, World Scientific) are extended, which require Γ to be Ahlfors-David regular.
KW - Cauchy transform
KW - Cauchy-Riemann operator
KW - Clifford analysis
UR - http://www.scopus.com/inward/record.url?scp=84869106118&partnerID=8YFLogxK
U2 - 10.1007/s00013-010-0140-2
DO - 10.1007/s00013-010-0140-2
M3 - Artículo
SN - 0003-889X
VL - 95
SP - 45
EP - 51
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 1
ER -