On the Existence of Radial Limits

Martha Guzmán-Partida; Carlos Robles-Corbala

doi:10.2478/tmmp-2014-0005

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On the Existence of Radial Limits

Tatra Mountains Mathematical Publications

Volume 58 (2014): Issue 1 (March 2014)

By: Martha Guzmán-Partida and Carlos Robles-Corbala

Open Access

|Aug 2014

Abstract

We discuss conditions that ensure the existence of radial limits a.e. for harmonic functions defined on the unit disc D. We give an example of a Banach-valued harmonic function without radial limits at almost every point on the boundary of D.

References

[1] ASH, J. M.-KARAEV, M. T.: On the boundary behavior of special classes of C∞ functions and analytic functions, Internat. Math. Forum 7 (2012), 153-166.
Search in Google Scholar
[2] BLASCO, O.: Radon-Nikodym versus Fatou, in: 29th National Congress of the Mexican Mathematical Society (F. Avila Murillo et al., eds.), San Luis Potosı, México, 1996. Sociedad Matem´atica Mexicana. Aportaciones Mat., Comun., Vol. 20, M´exico City, 1997, pp. 71-76.
Search in Google Scholar
[3] CONWAY, J. B.: Functions of One Complex Variable II, in: Grad. Texts in Math., Vol. 159, Springer-Verlag, New York, 1995.10.1007/978-1-4612-0817-4
Search in Google Scholar
[4] DIESTEL, J.-UHL, J. J.: Vector Measures, in: Math. Surveys Monogr., Vol. 15, AMS, Providence, R.I., 1977.10.1090/surv/015
Search in Google Scholar
[5] FATOU, P.: S´eries trigonom´etriques et s´eries de Taylor, Acta Math. 30 (1906), 335-400.10.1007/BF02418579
Search in Google Scholar
[6] SILVERMAN, R. A.: Complex Analysis with Applications. Prentice Hall, Englewood Cliffs, N. J., 1974.
Search in Google Scholar
[7] STEIN, E. M.-SHAKARCHI, R.: Real Analysis.Measure Theory, Integration, andHilbert Spaces, in: Princeton Lect. Anal., Vol. 3, Princeton University Press, Princeton, NJ, 2005.
Search in Google Scholar
[8] ZYGMUND, A.: Trigonometric Series (3rd ed.), in: Cambridge Math. Lib. (With a foreword by R. Fefferman), Cambridge University Press, Cambridge, 2002.
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2014-0005 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 47 - 51

Submitted on: Jul 24, 2013

Published on: Aug 15, 2014

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

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© 2014 Martha Guzmán-Partida, Carlos Robles-Corbala, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2014): Issue 1 (March 2014)