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Results in Mathematics

, Volume 72, Issue 1–2, pp 105–124 | Cite as

Tangential Cauchy–Riemann Equations on Pseudoconvex Boundaries of Finite and Infinite Type in \(\mathbb {C}^2\)

  • Ly Kim Ha
Article

Abstract

In this paper, we will present what we think is a natural extension of the finite type condition in the sense of Range on pseudoconvex domains. This type condition generalizes the notion of finite type in the original theory as well as consists many cases of infinite type in the sense of Range. Following the integral representation by Henkin, we also provide \(L^p\) and “new” Hölder estimates for solutions of \(\bar{\partial }_b\)-equations on the boundaries of domains which emphasize the infinite type condition.

Keywords

Pseudoconvex domains \(\bar{\partial }_b\)-operator integral representation \(\bar{\partial }_b\)-solutions range’s type Bochner–Martinelli–Koppelman operators 

Mathematics Subject Classification

Primary 32W10 Secondary 32F17 32T25 32V15 32T25 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceUniversity of Science, Vietnam National University HoChiMinh City (VNU-HCM)Ho Chi Minh CityVietnam

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