Cauchy-type integrals in several complex variables
We present the theory of Cauchy–Fantappié integral operators, with emphasis on the situation when the domain of integration, D , has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel i...
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| Published in: | Bulletin of mathematical sciences Vol. 3; no. 2; pp. 241 - 285 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cham
Springer International Publishing
01.08.2013
World Scientific Publishing Co. Pte., Ltd |
| Subjects: | |
| ISSN: | 1664-3607, 1664-3615 |
| Online Access: | Get full text |
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| Summary: | We present the theory of Cauchy–Fantappié integral operators, with emphasis on the situation when the domain of integration,
D
, has minimal boundary regularity. Among these operators we focus on those that are more closely related to the classical Cauchy integral for a planar domain, whose kernel is a holomorphic function of the parameter
z
∈
D
. The goal is to prove
L
p
estimates for these operators and, as a consequence, to obtain
L
p
estimates for the canonical Cauchy–Szegö and Bergman projection operators (which are not of Cauchy–Fantappié type). |
|---|---|
| Bibliography: | SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 |
| ISSN: | 1664-3607 1664-3615 |
| DOI: | 10.1007/s13373-013-0038-y |