On the singular Bochner-Martinelli integral

Citation
R. Rocha-chavez et al., On the singular Bochner-Martinelli integral, INTEG EQ OP, 32(3), 1998, pp. 354-365
Citations number
7
Categorie Soggetti
Mathematics
Journal title
INTEGRAL EQUATIONS AND OPERATOR THEORY
ISSN journal
0378620X → ACNP
Volume
32
Issue
3
Year of publication
1998
Pages
354 - 365
Database
ISI
SICI code
0378-620X(199811)32:3<354:OTSBI>2.0.ZU;2-H
Abstract
The Bockner-Martinelli (B.-M.) kernel inherits, for n greater than or equal to 2, only some of properties of the Cauchy kernel in C. For instance it i s known that the singular B.-M. operator M-n is not an involution for n gre ater than or equal to 2. M. Shapiro and N. Vasilevski found a formula for ( 2)(M2) using methods of quaternionic analysis which are essentially complex -twodimensional. The aim of this article is to present a formula for M-n(2) for any n greater than or equal to 2. We use now Clifford Analysis but for n = 2 our formula coincides, of course, with the above-mentioned one.