Global Regularity for the∂-b-Equation onCRManifolds of Arbitrary Codimension-Reference-Cited by-同舟云学术

Global Regularity for the∂-b-Equation onCRManifolds of Arbitrary Codimension

Published:2014 Issue: Volume:2014 Page:1-11
ISSN:1085-3375
Container-title:Abstract and Applied Analysis
language:en
Short-container-title:Abstract and Applied Analysis

Author:

Khidr Shaban¹²,Abdelkader Osama³

Affiliation:

1. Mathematics Department, Faculty of Science, King Abdulaziz University, North Jeddah, Jeddah 21589, Saudi Arabia

2. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef 62511, Egypt

3. Mathematics Department, Faculty of Science, Minia University, El-Minia 61915, Egypt

Abstract

LetMbe aC∞compactCRmanifold ofCR-codimensionl≥1andCR-dimensionn-lin a complex manifoldXof complex dimensionn≥3. In this paper, assuming thatMsatisfies conditionY(s)for someswith1≤s≤n-l-1, we prove anL2-existence theorem and global regularity for the solutions of the tangential Cauchy-Riemann equation for(0,s)-forms onM.

Funder

Deanship of Scientific Research, King Abdulaziz University, Jeddah

Publisher

Hindawi Limited

Subject

Applied Mathematics,Analysis

Link

http://downloads.hindawi.com/journals/aaa/2014/326434.pdf

Reference20 articles.

1. On the Extension of Holomorphic Functions from the Boundary of a Complex Manifold

2. L 2 estimates and existence theorems for the tangential Cauchy-Riemann complex

3. Sobolev estimates for the Lewy operator on weakly pseudo-convex boundaries

4. The range of the tangential Cauchy-Riemann operator

5. Global regularity for ∂¯b on weakly pseudoconvex CR manifolds

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