One-sided extendability of bounded functions

Abstract

In this paper, we show that one-sided extendability of functions in certain \(L^{\infty }\) spaces of a rectifiable Jordan arc is a rare phenomenon. We also discuss possible generalizations.

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Acknowledgements

The authors thank the referee for a careful reading of the paper and for several helpful suggestions which improved its exposition. Konstantinos Maronikolakis acknowledges financial support from the Irish Research Council.

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Correspondence to Myrto Manolaki.

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Manolaki, M., Maronikolakis, K. & Nestoridis, V. One-sided extendability of bounded functions. Complex Anal Synerg 7, 15 (2021). https://doi.org/10.1007/s40627-021-00076-x

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Keywords

  • \(L^\infty \) spaces
  • Holomorphic extensions
  • Non-tangential limits

Mathematics Subject Classification

  • 30H05
  • 30B30