Solutions to $ar{partial}$-equations on strongly pseudo-convex domains with $L^p$-estimates
We construct a solution to the $ar{partial}$-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type $(0,s)$, $sgeq 1 $, with values in a holomorphic vector bundle which is Nakano positive and for complex valued forms of type $(r,s)$, $1leq rleq n$, when the...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
Texas State University
2004-05-01
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Series: | Electronic Journal of Differential Equations |
Subjects: | |
Online Access: | http://ejde.math.txstate.edu/Volumes/2004/73/abstr.html |
Summary: | We construct a solution to the $ar{partial}$-equation on a strongly pseudo-convex domain of a complex manifold. This is done for forms of type $(0,s)$, $sgeq 1 $, with values in a holomorphic vector bundle which is Nakano positive and for complex valued forms of type $(r,s)$, $1leq rleq n$, when the complex manifold is a Stein manifold. Using Kerzman's techniques, we find the $L^p$-estimates, $1leq pleq infty$, for the solution. |
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ISSN: | 1072-6691 |