Weighted Sobolev L^p estimates for homotopy operators on strictly pseudoconvex domains with C² boundary

2019/06/29 by Ziming Shi, Shi, Ziming
Computer Science · Mathematics · #32A26 #32T15 #32W05 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1907.00264

openalex publication_date 2019/06/29 · openalex created_date 2019/07/12 · openalex updated_date 2026/08/01

Abstract

We derive estimates in a weighted Sobolev space W^k,p_μ(D) for a homotopy operator on a bounded strictly pseudoconvex domain D of C² boundary in \Cⁿ. As a result, we show that given any 2n < p < ∞, k > 1, q ≥ 1, and a \dbar-closed (0,q) form \var of class W^k,p(D), there exist a solution u to \dbar u = \var such that u ∈ W^k,p_\yh-\ve(D) for any \ve > 0. If k=1, then we can take p to be any value between 1 and ∞. In other words, the solution gains almost \yh-derivative in a suitable sense.

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