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On the Notion of the Bochner–Martinelli Integral for Domains with Rectifiable Boundary

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On the Notion of the Bochner–Martinelli Integral for Domains with Rectifiable Boundary

Content Provider	Springer Nature Link
Author	Abreu Blaya, Ricardo Bory Reyes, Juan Shapiro, Michael
Copyright Year	2007
Abstract	In this paper we discuss the notion of the Bochner–Martinelli kernel for domains with rectifiable boundary in $${\mathbb{C}}^2 $$ , by expressing the kernel in terms of the exterior normal due to Federer (see [17,18]). We shall use the above mentioned kernel in order to prove both Sokhotski–Plemelj and Plemelj–Privalov theorems for the corresponding Bochner–Martinelli integral, as well as a criterion of the holomorphic extendibility in terms of the representation with Bochner–Martinelli kernel of a continuous function of two complex variables.Explicit formula for the square of the Bochner–Martinelli integral is rediscovered for more general surfaces of integration extending the formula established first by Vasilevski and Shapiro in 1989.The proofs of all these facts are based on an intimate relation between holomorphic function theory of two complex variables and some version of quaternionic analysis.
Starting Page	143
Ending Page	168
Page Count	26
File Format	PDF
ISSN	16618254
Journal	Complex Analysis and Operator Theory
Volume Number	1
Issue Number	2
e-ISSN	16618262
Language	English
Publisher	Birkhäuser-Verlag
Publisher Date	2007-01-19
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Quaternionic analysis Bochner–Martinelli integral rectifiability $H^p$-spaces, Nevanlinna spaces Functions of hypercomplex variables and generalized variables Other generalizations of function theory of one complex variable Integral representations; canonical kernels Mathematics Operator Theory Analysis
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Theory and Mathematics Computational Mathematics

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