The Boundary Behavior of Self-Conjugate Differential Forms in \(C^1\)-domains
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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.
KeywordsSelf-conjugate differential forms Trace theorems Cauchy integral Plemelj formulas Riesz inequalities
Mathematics Subject ClassificationPrimary 42B99 Secondary 31C99 47G10 58A10
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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