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Complex Analysis and Operator Theory

, Volume 13, Issue 2, pp 563–582 | Cite as

The Boundary Behavior of Self-Conjugate Differential Forms in \(C^1\)-domains

  • Francesco SilverioEmail author
Article
  • 38 Downloads

Abstract

This paper deals with the boundary behavior of self-conjugate differential forms. In particular, we state and prove trace theorems and Plemelj-type formulas in \(C^1\)-domains; some remarkable consequences of these results are discussed too. As a further goal, we obtain boundary inequalities extending the classical M. Riesz theorem for conjugate functions.

Keywords

Self-conjugate differential forms Trace theorems Cauchy integral Plemelj formulas Riesz inequalities 

Mathematics Subject Classification

Primary 42B99 Secondary 31C99 47G10 58A10 

Notes

Acknowledgements

This paper is part of the author’s Ph.D. thesis, written under the supervision of Prof. Alberto Cialdea at University of Basilicata and University of Salento. The author wishes to tank Prof. Alberto Cialdea for valuable comments and suggestions.

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Sala ConsilinaItaly

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