Hölder estimates for homotopy operators on strictly pseudoconvex domains with C 2 boundary

We derive a new homotopy formula for a strictly pseudoconvex domain of C2 boundary in Cn by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r>1 and q>0, we obtain a Λr+1/2 solution u to ∂¯u=f for a ∂¯-closed (0, q)-form f of class Λr in...

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Bibliographic Details
Published in:Mathematische annalen 2019-01, Vol.374 (1), p.841-880
Main Author: Gong, Xianghong
Format: Article
Language:English
Subjects:
Domains
Estimates
Operators
Online Access:Get full text
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Summary:We derive a new homotopy formula for a strictly pseudoconvex domain of C2 boundary in Cn by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators. For r>1 and q>0, we obtain a Λr+1/2 solution u to ∂¯u=f for a ∂¯-closed (0, q)-form f of class Λr in the domain. We apply the estimates to obtain boundary regularities of D-solutions for a domain in Cn×Rm.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-018-1693-9