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Analytic functions in Smirnov classes \(E^p\) with real boundary values II

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Abstract

Multiply connected Smirnov domains with non-smooth boundaries may admit non-trivial functions of Smirnov class \(E^p\) with real boundary values for certain \(p\ge 1\). This paper describes the particular geometric boundary characteristics of multiply connected Smirnov domains that make the existence of such functions possible. This extends the similar results in De Castro and Khavinson (2012) obtained for simply connected domains.

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References

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Acknowledgments

Both authors are indebted to Razvan Teodorescu for valuable insights regarding Sect. 3. We also gratefully acknowledge partial support from the National Science Foundation under the grants DMS-0855597 and DMS-1019602.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of South Florida, 4202 E Fowler Ave, CMC342, Tampa, FL, 33620-5700, USA

    Lisa De Castro & Dmitry Khavinson

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  1. Lisa De Castro
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  2. Dmitry Khavinson
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Correspondence to Lisa De Castro.

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De Castro, L., Khavinson, D. Analytic functions in Smirnov classes \(E^p\) with real boundary values II. Anal.Math.Phys. 3, 21–35 (2013). https://doi.org/10.1007/s13324-012-0036-3

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