TY - JOUR
T1 - Minkowski dimension and cauchy transform in Clifford analysis
AU - Blaya, Ricardo Abreu
AU - Reyes, Juan Bory
AU - García, Tania Moreno
PY - 2007/8
Y1 - 2007/8
N2 - In the present paper we provide some conditions of a geometrical character for continuous extendibility of the Clifford-Cauchy transform to the boundary of a domain in the Euclidean space of higher dimensions if its density satisfies a Hölder condition. The criterion obtained in this work is an extension to a very general class of domains of a result, which has already become classical, obtained by Viorel Iftimie, who proved in 1965, for the case of a domain with compact Liapunov boundary, that the Clifford-Cauchy transform has Hölder-continuous limit values for any Hölder-continuous density.
AB - In the present paper we provide some conditions of a geometrical character for continuous extendibility of the Clifford-Cauchy transform to the boundary of a domain in the Euclidean space of higher dimensions if its density satisfies a Hölder condition. The criterion obtained in this work is an extension to a very general class of domains of a result, which has already become classical, obtained by Viorel Iftimie, who proved in 1965, for the case of a domain with compact Liapunov boundary, that the Clifford-Cauchy transform has Hölder-continuous limit values for any Hölder-continuous density.
KW - Cauchy transform
KW - Clifford analysis
KW - Geometric measure theory
UR - http://www.scopus.com/inward/record.url?scp=34548065501&partnerID=8YFLogxK
U2 - 10.1007/s11785-007-0015-0
DO - 10.1007/s11785-007-0015-0
M3 - Artículo
AN - SCOPUS:34548065501
SN - 1661-8254
VL - 1
SP - 301
EP - 305
JO - Complex Analysis and Operator Theory
JF - Complex Analysis and Operator Theory
IS - 3
ER -