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

Tangential Cauchy–Riemann Equations on Pseudoconvex Boundaries of Finite and Infinite Type in... 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 $$L^p$$ L p and “new” Hölder estimates for solutions of $$\bar{\partial }_b$$ ∂ ¯ b -equations on the boundaries of domains which emphasize the infinite type condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Results in Mathematics Springer Journals

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

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### 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 $$L^p$$ L p and “new” Hölder estimates for solutions of $$\bar{\partial }_b$$ ∂ ¯ b -equations on the boundaries of domains which emphasize the infinite type condition.

### Journal

Results in MathematicsSpringer Journals

Published: Nov 30, 2016

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