Weighted C^k estimates for a class of integral operators on non-smooth domains

2009/03/24 by Dariush Ehsani, Ehsani, Dariush
Mathematics · #32A25 #32W05 #35B65 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CV #msc:32A25 #msc:32W05 #msc:35B65

paper · pdf · doi:10.48550/arxiv.0903.4082

32 pages

arxiv created 2009/03/24 · openalex publication_date 2009/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We apply integral representations for (0,q)-forms, q≥1, on non-smooth strictly pseudoconvex domains, the Henkin-Leiterer domains, to derive weighted C^k estimates for a given (0,q)-form, f, in terms of C^k norms of \mdbar f, and \mdbar^∗ f. The weights are powers of the gradient of the defining function of the domain.

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