TY - JOUR
T1 - The Bochner-Martinelli transform with a continuous density
T2 - Davydov's theorem
AU - Abreu-Blaya, Ricardo
AU - Bory-Reyes, Juan
AU - Pena-Pena, Dixan
N1 - Funding Information:
This paper was written while the second author was visiting the Department of MathematicalAnalysis of Ghent University. He was supported by the Special Research Fund No. 01T13804, obtained for collaboration between the Clifford Research Group in Ghent and the Cuban Research Group in Clifford analysis, on the subject Boundary values theory in Clifford Analysis. Juan Bory Reyes wishes to thank all members of this Department for their kind hospitality. Dixan Peña Peña was supported by a Doctoral Grant of the Special Research Fund of Ghent University. He would like to express his sincere gratitude. The authors acknowledge the valuable suggestions and comments of both referees, which turned out to be helpful in improving this paper.
PY - 2008
Y1 - 2008
N2 - In this paper, we extend to the theory of functions of several complex variables, a theorem due to Davydov from classical complex analysis. We prove the following: if n is a bounded domain with boundary of finite (2n-1)-dimensional Hausdorff measure H2n-1 and f is a continuous complex-valued function on such that [image omitted] converges uniformly on as r0, then the Bochner-Martinelli transform on of f admits a continuous extension to and the Sokhotski-Plemelj formulae hold. For n=2, we briefly sketch how quaternionic analysis techniques may be used to give an alternative proof of the above result.
AB - In this paper, we extend to the theory of functions of several complex variables, a theorem due to Davydov from classical complex analysis. We prove the following: if n is a bounded domain with boundary of finite (2n-1)-dimensional Hausdorff measure H2n-1 and f is a continuous complex-valued function on such that [image omitted] converges uniformly on as r0, then the Bochner-Martinelli transform on of f admits a continuous extension to and the Sokhotski-Plemelj formulae hold. For n=2, we briefly sketch how quaternionic analysis techniques may be used to give an alternative proof of the above result.
KW - Bochner-Martinelli transform
KW - Non-smooth boundaries
KW - Sokhotski-Plemelj formulae
UR - http://www.scopus.com/inward/record.url?scp=54749134575&partnerID=8YFLogxK
U2 - 10.1080/10652460802128567
DO - 10.1080/10652460802128567
M3 - Artículo
SN - 1065-2469
VL - 19
SP - 613
EP - 620
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
IS - 9
ER -