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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Springer-Verlag GmbH Germany, part of Springer Nature 2020
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/s40315-019-00297-6
- Publisher site
- See Article on Publisher Site
Abstract
In the present paper we study the boundary behavior of a weighted Koppelman type integral with a specific choice of weight for a function ϕ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\phi $$\end{document} that is integrable on a bounded domain D⊂Cn\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$D\subset \mathbb {C}^n$$\end{document} and is continuous on its C1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathcal {C}^1$$\end{document}-boundary. Applying the above results, we derive a variation of Hartogs phenomena about the holomorphicity of a function ϕ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\phi $$\end{document} which is integrable in a D and continuous on ∂D\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\partial D$$\end{document}, provided that it satisfies, in some sense, a stronger version of “one-dimensional holomorphic continuation property” along any complex line meeting the domain.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Mar 2, 2020