Regularity for the CR vector bundle problem II

2009/11/24 by Xianghong Gong, Gong, Xianghong, S. M. Webster +1 · 1 citation
Mathematics · #32V05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32V05

paper · pdf · doi:10.48550/arxiv.0911.4549

arxiv created 2009/11/24 · arxiv updated 2009/12/08

Abstract

We derive a \mathcal C^k+\yt Hölder estimate for Pϕ, where P is either of the two solution operators in Henkin's local homotopy formula for ∂_b on a strongly pseudoconvex real hypersurface M in \mathbf Cⁿ, ϕ is a (0,q)-form of class \mathcal C^k on M, and k≥0 is an integer. We also derive a \mathcal C^a estimate for Pϕ, when ϕ is of class \mathcal C^a and a≥0 is a real number. These estimates require that M be of class \mathcal C^k+5/2, or \mathcal C^a+2, respectively. The explicit bounds for the constants occurring in these estimates also considerably improve previously known such results. These estimates are then applied to the integrability problem for CR vector bundles to gain improved regularity. They also constitute a major ingredient in a forthcoming work of the authors on the local CR embedding problem.

Cited by

• Integrability of Koszul connections on complex vector bundles over domains in \mathbf Cⁿ

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