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Global boundary regularity for the $ \bar \partial $ ‐equation on q ‐pseudoconvex domains
Author(s) -
Ahn Heungju
Publication year - 2007
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200410486
Subject(s) - bounded function , mathematics , domain (mathematical analysis) , bar (unit) , boundary (topology) , mathematical analysis , pure mathematics , physics , meteorology
We introduce a notion of q ‐pseudoconvex domain of new type for a bounded domain of ℂ n and prove that for given a $ \bar \partial $ ‐closed ( p, r )‐form, r ≥ q , that is smooth up to the boundary, there exists a ( p , r – 1)‐form smooth up to the boundary which is a solution of $ \bar \partial $ ‐equation on a bounded q ‐pseudoconvex domain. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)